Publication List
Publications in Refereed Journals:
Papers accepted
 (with Azahara Delatorre, W. Ao and Mar Gonzalez)
A gluing approach for the fractional Yamabe problem with isolated singularities Crelle's Journal
accepted for publication
 (W. Ao, Hardy Chan and Mar Gonzalez)
Existence of positive weak solutions for fractional LaneEmden equations with prescribed singular sets CVPDE
accepted for publication
 (with Yong Liu)
Nondegeneracy of the traveling lump solution to the $2+1$ Toda lattice Journal of Math Physics
accepted for publication
 (with Fanghua Lin)
Superfluids passing an obstacle and vortex nucleation
DCDSA (special volume for L. Caffarelli's 70th birthday)
accepted for publication
 (with Chang, Tzou and Ward)
Refined Stability Thresholds for Localized Spot Patterns for the Brusselator Model in $R^2$
European J. Appl. Math.
accepted for publication
 (with ZM Guo, X. Huang and LP Wang) On Delaunay solutions of a biharmonic elliptic equation with critical exponent
Journal d'Analyse Mathematique
accepted for publication
 (with T. Kolokolnikov, J. Tzou and M. Ward)
Stabilizing a homoclinic stripe
Philosophical Transactions A of the Royal Society
accepted for publication
 (with Y. Liu)
On Helmholtz equation and Dancer's type entire solutions for nonlinear elliptic equations
Proc. Amer. Math. Soc.
accepted for publication
 (with W. Ao and M. Winter)
Stable boundary spike clusters for the twodimensional GiererMeinhardt system
J. Math. Pure Appl.
accepted for publication
 (with Wen Yang)
Multibump ground states of the fractional GiererMeinhardt system on the real line
J. Dyn. Diff. Eqns.
accepted for publication
 (with H. Chan)
On De Giorgi's Conjecture: recent progress and open problems
Science in China: Mathematics
accepted for publication
 (with Lei Zhang)
Nondegeneracy of Gauss curvature equation with negative conic singularity
Pacific Journal of Mathematics
accepted for publication

(with Y. Sire and Y. Zheng)
Nondegeneracy of halfharmonic maps from $R$ into $S^1$
Proc. AMS
accepted for publication

(with Kelei Wang)
Finite Morse index implies finite ends
Comm. Pure Appl. Math.
accepted for publication
 (with W. Ao and M. Musso)
Nondegeneracy of nonradial signchanging solutions to the nonlinear Schrodinger equations
Bulletin de la SMF
accepted for publication
 (with Y. Guo, S. Li and X. Zeng) Ground states of twocomponent attractive BoseEinstein condensates II: Semitrivial limit behavior
Transc. of AMS
accepted for publication

(with M. Musso and S. Deng)
Signchanging blowup solutions for Yamabe problem
International Math. Research Notes (IMRN)
accepted for publication
 (with Kelei Wang)
On Serrin's overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg
Comm. PDE
accepted for publication
 (with Manuel del Pino, M. Musso, C. Roman)
Interior bubbling solutions for the critical LinNiTakagi problem in dimension 3
Journal d'Analyse Mathematique
accepted for publication
 (with Y. Sire)
On a fractional Henon equation and applications
Math Research Letters
accepted for publication
 (with Yanyan Li and H. Xu)
Multibump solutions of $\Delta u
=K(x)u^{\frac{n+2}{n2}}$ on Lattices in ${\mathbb R}^n$
Journal fur die reine und ang. Math. (Crelle's Journal)
accepted for publication
 (with X.Ren)
A toroidal tube solution of a nonlocal geometric
problem
Interfaces and Free Boundaries accepted for publication.
2018
 (with W. Ao and H. Chan)
Boundary concentrations on segments
for the LinNiTakagi problem
Annali della Scuola Normale Superiore di Pisa
18 (2018), no. 2, 653696.
 (with Juan Davila and Manuel del Pino)
Nonlocal $s$minimal surfaces and Lawson cones
Journal of Differential Geometry
109(2018), 111175
 (with A. Jevnikar and W. Yang)
On the topological degree of the mean field equation with two parameters
Indiana Univ. Math. Journal
67(2018), Vol. 1, 2988.
 (with A. Jevnikar and W. Yang)
Classification of blowup limits for the SinhGordon equation
Diff. Int. Equations
31 (2018), no. 910, 657684.
 (with S. Kim and M. Musso)
Existence theorems of the fractional Yamabe problem
Analysis & PDE
11(2018), no.1, 75113.
 (with H. Kikuchi)
Bifurcation diagram of solutions to elliptic equation with exponential nonlinearity in higher dimensions
Proc. Eding. Math. A.
148 (2018), no. 1, 101122.
 (with T. Kolokolnikov)
Pattern formation in a reactiondiffusion system with spacedependent feed rate
SIAM Review
60 (2018), no. 3, 626645.
 (with CS Lin and Z. Nie)
Toda system and hypergeometric equations Transcations of American Math Society
370 (2018), no. 11, 76057626.

(with CS Lin, Y. Lee and W. Yang)
Degree counting and shadow system for $SU(3)$ Toda system: one bubbling
Journal of Differential Equations
264 (2018), no. 7, 43434401.
 (with CS Lin, W. Yang and L. Zhang)
On rank two Toda system with arbitrary singularities: local max and new estimates Analysis & PDE
11 (2018), no.4, 873898.
 (with Yong Liu and Kelei Wang)
On a free boundary problem and minimal surfaces Annals IHPANL
35(2018), no. 4, 9931017.
 (with N. T. Fadai and M. Ward)
A timedelay in the activator knetics enhances the stability of a spike solution to the GiererMeinhardt model
DCDSB
23(2018), no.4, 14311458.

(with Justin Tzou and M. Ward)
Anomalous Scaling of Hopf Bifurcation Thresholds for the Stability of
Localized Spot Patterns for ReactionDiffusion Systems in 2D
SIAM Journal of Applied Dynamical Systems
17(2018), no. 11, 9821022.
2017
 (with A. de la Torre, M. del Pino, Mar del mar Gonzalez)
Delaunaytype singular solutions for the fractional Yamabe problem
Math Annalen
369 (2017), no. 12, 597626.
 (with W. Ao and W. Yang)
Infinitely many positive solutions of fractional nonlinear Schr$\ddot{\mathrm{O}}$dinger equations with nonsymmetric potentials
DCDSA
37 (2017), no. 11, 55615601.
 (with Hardy Chan)
Travelling wave solutions for bistable fractional AllenCahn equations with a pyramidal front.
Journal of Differential Equations
262 (2017), no. 9, 45674609.
 (with Juan Davila and L. Dupaigne)
On the fractional LaneEmden equation
Trans. Amer. Math. Soc.
369 (2017), no. 9, 60876104.
 (with M. del Pino and O.Agudelo)
Catenoidal layers for the AllenCahn equation in bounded domains
Chinese Annals of Mathematics (a special volume for Professor H. Brezis' 70th birthday)
38 (2017), no. 1, 1344.
 (with Y. Ding)
Multiplicity of semiclassical solutions
to nonlinear Schr¨odinger equations J.Fixed Point Theory Appl. (special volume in honor of Professor Paul Rabinowitz's 75th birthday)
19 (2017), no. 1, 9871010.
 (with N. T. Fadai and M.J. Ward)
Delayed reactionkinetics and the stability of spikes in the GiererMeinhardt system
SIAM Journal Applied Math
77(2017), no.2, 664696.
 (with M. Fazly)
On finite Morse index solutions of higher order fractional LaneEmden equation
American Journal of Mathematics
139 (2017), no. 2, 433460
 (with Changfeng Gui and Yong Liu) Twoend solutions to the AllenCahn equation in $\mathbb{R}^3$
Advances in Math
320C (2017), 926992.
 (with Yujin Guo and CS Lin)
Local uniqueness and refined spike profiles of ground states for twodimensional attractive BoseEinstein condensates
SIAM J. Math. Anal.
49 (2017), no. 5, 36713715
 (with ZM Guo and Feng Zhou)
Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation
J. Diff. Eqns.
263 (2017), no. 2, 11881224.
 (with S. Kim and M. Musso)
A noncompactness result on the fractional Yamabe problem in large dimensions
and supplement material Journal of Functional Analysis
273 (2017), no. 12, 37593830.
 (with Yong Liu and Kelei Wang)
Global minimizers of AllenCahn equation in dimensions $ n\geq 8$ J.Math Pure Appl.
108 (2017), no. 6, 818840.
 (with S Luo and W. Zou)
On a transcendental equation involving quotients of Gamma functions Proc. AMS
145(2017), no. 6, 26232637.

(with X. Ren)
The spectrum of the torus profile to a geometric variational problem with long range interaction
Physica D: Nonlinear Phenomena
351/352 (2017), 6288.
 (with M. Winter)
Stable spike clusters for the onedimensional GiererMeinhardt system
European Journal of Applied Math
28 (2017), no. 4, 576635
 (with M. Winter and W. Yang)
Stable spike clusters for the precurson GiererMeinhardt system in $R^2$
CVPDE
56 (2017), no. 5, 56:142
2016
 (with M. del Pino and O.Agudelo)
Higher dimensional catenoid, Liouville equation and AllenCahn equation Liouville's equation
International Math. Research Note (IMRN)
2016, no. 23, 70517102
 (with WW Ao and CS Lin)
On Nontopological Solutions of the $A_2$ and $B_2$
ChernSimons System (112 pages)
Memoirs of American Mathematical Society
239(2016), no. 1132.
 (with WW Ao and CS Lin)
On nontopological solutions of the $G_2$ ChernSimons system
Communications Analysis and Geometry
24 (2016), no. 4, 717752.
 (with WW Ao, M. Musso and F. Pacard)
Solutions without any symmetry for semilinear elliptic problems
Journal of Functional Analysis
270(2016), no.3, 884956.
 (with W. Ao and W. Yao)
Uniqueness and nondegeneracy of signchanging radial solutions of an almost critical problem
Advances in Differential Equations
21(2016), no.1112, 10491084.
 (with Juan Davila and Kelei Wang)
Qualitative Analysis of Rupture Solutions for an MEMS Problem
Ann.Inst. Henri.Poincare NonLinearie
33(2016), no.1, 221242
 (with Z.Du)
Clustering layers for the FifeGreenlee problem in $\mathbb{R}^n$
Proc. Royal Soc. Edin. Math Section A
146(2016), no. 1, 107139.
 (with Z. Du, C. Gui and Y. Sire)
Layered solutions for a fractional inhomogeneous AllenCahn equation
NoDEA
23(2016), no.3, 23:29
 (with Changfeng Gui and Yong Liu) On variational characterization of fourend solutions of the AllenCahn equation in the plane
Journal of Functional Analysis
271(2016), no. 10, 26732700.
 (with ZM Guo and Wen Yang)
On nonradial singular solutions of supercritical biharmonic equations
Pacific Journal of Math.
284(2016), no.2, 395430.
 (with M. Fazly)
On stable solutions of the fractional HenonLaneEmden equation
Comm. Contemp. Math.
18(2016), No. 5, 1650005 (24pages)
 (with Meiyue Jiang and Liping Wang)
$2\pi$periodic selfsimilar solutions for the anisotropic affine curve
shortening problem II
DCDSA
36(2016), no.2, 785803.
 (with CS Lin and L. Zhang)
Local profile of fully bubbling solutions to SU(n+1) Toda Systems
Journal of Europ.Math. Soc. (JEMS)
18(2016), no. 8, 17071728.
 (with Bruno Premoselli)
Noncompactness and infinite number of conformal initial data sets in high dimensions
Journal of Functional Analysis
270(2016), no.2, 718747.
 (with M. Musso)
Signchanging blowingup solutions for supercritical BahriCorn's problem
CVPDE
55(2016), no.1, 55:1
 (with A. Pistoia and M. Musso) New blowup phenomena for {\em SU(n+1)} Toda system
JDE
260(2016), no. 7, 62326266.
 (with M. Musso and S. Yan)
Infinitely many positive solutions for an nonlinear field equation
with supercritical growth
Proceedings of London Math Society
112(2016), no.1, 126.
 (with S. Santra)
Positive solutions of nonlinear Schrodinger equation with peaks on a Clifford torus
Mathematische Nachrichten
289(2016), no. 89, 11311147.
 (with Santra)
On a singular perturbed problem in an annulus
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
(5)15(2016), 837857
 (with Kelei Wang)
On the uniqueness of solutions of an nonlocal elliptic system
Math. Annalen
365(2016), no.12, 105153.
 (with Jun Yang)
Traveling vortex helicies for Schr\"odinger Map Equation
Transc. of Amer. Math. Soc.
368(2016), no.4, 25892622.
2015
 (with WW Ao and CS Lin)
On Toda system with Cartan matrix $G_2$
Proc. Amer. Math. Soc.
143(2015), no.8, 35253536.
 (with M. del Pino and O. Agudelo)
Multiple Catenoidal End Solutions to the AllenCahn
Equation in $\R^3$
J. Math. Pures Appl.
103(2015), no.1, 142218
 (with M. del Pino and F. Pacard)
Serrin's overdetermined problems and constant mean curvature surfaces
Duke Math Journal
164(2015), no.14, 26432722.
 (with M. del Pino and Wei Yao)
Intermediate Reduction Methods and Infinitely many positive solutions of nonlinear Schr\"{o}dinger equations with nonsymmetric potentials
Cal.Var. PDE
53(2015), no.12, 473523.
 (with M. Fazly and X. Xu)
A pointwise inequality for the fourth order LaneEmden equation
Analysis & PDE
8(2015), no. 7, 15411563.
 (with M. Grossi and F. Gladiali) On a general $SU(3)$ Toda system
CVPDE
54(2015), no.4, 33533372.
 (with D. Iron, J. Rumsey, M.J. Ward)
On accurately estimating stability threshold for periodic spot patterns of reactiondiffusion systems in $R^2$
European Journal of Applied Math
26(2015), no.3, 325353.
 (with M. Kowalczyk and Yong Liu)
Singly periodic solutions of the AllenCahn equation and the Toda lattice
Comm. Part. Diff. Eqns.
40(2015), no.2, 329356.
 (with M. Kowalczyk, Yong Liu and Frank Pacard)
Endtoend construction for the AllenCahn equation in the plane
Cal. Var. PDE
52(2015), no.2, 329356.
 (with CS Lin and L. Zhang)
Classification of blowup limits for $SU(3)$ singular Toda systems
Analysis and PDE
8(2015), no. 4, 807837.
 (with CS Lin and L. Zhang)
Convergence rate, location and $\partial_z^2$ condition for fully bubbling solutions to $SU(n+1)$ Toda systems
Advances in Mathematics
285(2015), 11891224.
 (with M. Musso)
Nondegeneracy of nonradial nodal solutions to Yamabe problem
Comm. Math. Physics
340(2015), no.3, 10491107
 (with Xiaofeng Ren) A double bubble assembly as a new phase of
a ternary inhibitory system
Arch Rat Mech Anal
215(2015), no.3, 9671034.
 (with Kelei Wang)
Analysis of Blowup Locus and Existence of Weak Solutions for Nonlinear Supercritical Problems
Int. Math. Res. Not. IMRN
2015, no.10, 26342670
 (with M. Winter)
Existence and stability of a spike in the central component for a consumer chain model
Journal of Dynamical and Differential Equations
27(2015), no.34, 11411171.
 (with S. Yan)
Clustered bubbles for An Elliptic problem with critical growth
Nonlinear Analysis:TMA
119(2015), 4661.
2014
 (with WW Ao)
Infinitely many positive solutions for nonlinear equations with nonsymmetric potential
Cal Var. PDE
51(2014), no.34, 761798.
 (with H. Berestycki and M. Winter)
Existence of Symmetric and Asymmetric Spikes for a Crime Hotspot Model
SIAM J. Math. Analysis
46(2014), no.1, 691719
 (with Juan Davila, Louis Dupaigne and Kelei Wang)
A Monotonicity Formula and a Liouvilletype Theorem for a Fourth Order Supercritical Problem
Advances in Mathematics
258(2014), 240285
 (with Juan Davila and Manuel del Pino)
Concentrating standing waves for the fractional nonlinear Schrodinger equation
J. Diff. Eqns.
256(2014), no.2, 858892.
 (with Daomin Cao and Z. Liu)
Regularization of point vortices pairs for the Euler equation in dimension two
Archive Rat. Mech. Anal.
212(2014), no.1, 179217
 (with Y.Guo and B. Li)
Entire nonradial solutions for noncooperative coupled elliptic system with critical exponents
J. Diff. Eqns.
256(2014), no. 10, 34633495
 (with ZM Guo)
Liouville Type Results and Regularity of the Extremal Solutions of Biharmonic equation with negative exponents
DCDSA 34(2014), no.6, 25612580.
 (with ZM Guo)
Rupture solutions of an elliptic equation with a singular nonlinearity
Proc. Roy. Soc. Edin., A 144(2014), no. 5, 905924.
 (with D. Iron, J. Rumsey and M. Ward )
Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for ReactionDiffusion Systems in $R^2$
Journal of Nonlinear Science
24(2014), no. 5, 857912.
 (with T. Kolokolnikov and A. Alcolado)
Basic mechanisms driving complex spike dynamics in a chemotaxis model with logistic growth.
SIAM Journal of Applied Mathematics
74(2014), no.5, 13751396.
 (with T. Kolokolnikov and M.J. Ward)
The stability of steadystate hotspot patterns for a reactiondiffusion model of urban crime
DCDSB 19(2014), no.5, 13731410.
 (with Xiaofeng Ren)
Double tori solution to an equation of mean curvature and Newtonian potential
Cal Var PDE
49(2014), no.34, 9871018
 (with Xiaofeng Ren) Asymmetric and symmetric double bubbles in
an inhibitory ternary system
SIAM J. Math. Anal.
46(2014), no.4, 27982852.
 ( with S. Santra)
Profile of the least energy solution of a singular perturbed Neumann problem with mixed powers
Annali di Matematica Pura ed Applicata
(4) 193(2014), no.1, 3970.
 (with M. Winter)
Stability of cluster solutions to a tritrophic food chain model
Journal of Mathematical Biology
68(2014), no.12, 139.
2013
 (with WW Ao and Jing Zeng)
An optimal bound on the number of
interior spike solutions for the LinNiTakagi problem
Journal of Functional Analysis
265 (2013), no. 7, 13241356.
 (with H. Berestycki, TCLin and CY Zhao) On PhaseSeparation Model: Asymptotics and Qualitative Properties
Archive Rational Mechanics Analysis 208(2013), no.1, 163200.
 (with H. Berestycki, S. Terracini and K. Wang)
On Entire Solutions of an Elliptic System Modeling Phase Separations
Advances in Mathematics
243(2013), pp. 102  126
 (with M. del Pino and M. Kowalczyk)
Traveling waves with multiple and nonconvex fronts for a bistable semilinear parabolic equation
Comm. Pure Appl. Math.
66(2013), no.4, 481547.
 (with M. del Pino and M. Kowalczyk)
Entire Solutions of the AllenCahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature
Journal of Differential Geometry 83(2013), no.1, 67131.
 (with Yanheng Ding and T. Xu)
Existence and concentration of semiclassical solutions for an
nonlinear MaxwellDirac system
Journal of Mathematical Physics
54(2013), no.6, 061505, 33pp.
 (with Yuxia Guo and B. Li)
Large energy entire solutions for the Yamabe type problem of polyharmonic operator
J. Diff. Eqns. 254(2013), no.1, 199228
 (with E. Hebey)
SchrodingerPoisson system in the 3sphere
Cal Var PDE 47(2013), no.12, 2554.
 (with Fouad Hadj Selem and Hiroaki Kikuchi)
Existence and uniqueness of singular solution
to stationary Schr\"{o}dinger equation with supercritical nonlinearity
DCDSA 33 (2013), no. 10, 46134626.
 (with T. Kolokolnikov and W. Yang)
On large ring solutions for GiererMeinhardt system in $R^3$
Journal of Differential Equations
255(2013), no.7, 14081436.
 (with TC Lin and Jun Yang)
Vortex rings for the GrossPitaevskii equation in $\R^3$
J. Math. Pures Appl. (9) 100(2013), no.1, 69112.
 (with L.Ma)
Stability and multiple solutions to
Einsteinscalar field Lichnerowicz equation on manifolds
J. Math. Pures App. (9)99(2013), no.2, 174186.
 (with Frank Pacard)
Stable solutions of the AllenCahn equation in dimension $8$ and minimal cones
Journal of Functional Analysis 264(2013), no.5, 11311167.
 (with Xiaofeng Ren)
A double bubble in a ternary system with long range interaction.
Archive Rational Mech. Analysis
208(2013), no.1, 201253.
 (with S. Santra)
New entire positive solution for the nonlinear Schr\"{o}dinger equation: Coexistence of fronts and bumps
American Journal of Mathematics
135(2013), no.2, 443491.
 (with F. Ting)
Multivortex nonradial solutions to the magnetic GinzburgLandau equations
Comm. Math. Phys. Volume 317, Issue 1 (2013), Page 6997
 (with L. Wang)
Infinite Multiplicity for an Inhomogeneous Supercritical Problem in Entire Space
Comm. Pure Appl. Anal.
12(2013), No. 3, 12431257.
 (with Kelei Wang)
On solutions with polynomial growth to an autonomous nonlinear elliptic problem
Advance Nonlinear Studies 13(2013), no.4, 921932.
 (with Xingwang Xu and Wen Yang)
On the classification of stable solution to biharmonic problems in large dimensions
Pacific Journal of Mathematics
263(2013), no.2, 495512.
 (with S. Yan )
Infinitely many nonradial solutions for the H\'enon equation with critical growth
Revista Matematica Iberoamericana 29(2013), no.3, 9971020
 (with Dong Ye)
Liouville Theorems for finite Morse index solutions of Biharmonic problem
Mathematische Annalen 356(2013), no.4, 15991612.
 (with C.Zhao)
Noncompactness of the Prescribing $Q$curvature problem in large dimensions
Cal. Var. PDE 46(2013), No.1, 123164
2012
 (with A. Aftalion and P. Mason)
Vortexpeak interaction and lattice shape in rotating twocomponent BoseEinstein condensates.
Physical Review A 85(2012), no.3, 033614.
 (with Wenyi Chen and S. Yan)
Infinitely many solutions for the Schr\"odinger equations in
$\R^N$ with critical growth
Journal of Differential Equations
252(2012), no.3, 24252447.
 (with J. Davila)
Point ruptures for a MEMS equation with fringing field
Comm. Part. Diff. Eqns. 37(2012), 14621493.
 (with EN Dancer and ZM Guo)
Nonradial singular solutions of LaneEmden
equation in $R^N$
Indiana Univ. Math. Journal 61(2012), no.5, 19711996.
 (with Manuel del Pino and Mike Kowalczyk)
On De Giorgi's conjecture and beyond
Proceedings of National Acad. of Sciences (PNAS) 109(2012), vol. 18, 68456850.
 (with E. Hebey)
Resonant states for the static KleinGordonMaxwellProca system
Math Research Letters 19(2012), no.4, 953967.
 (with ChangShou Lin and Dong Ye)
Classification and nondegeneracy of $SU(n+1)$ Toda system with singular sources Inventiones Mathematicae 190(2012), no.1, 169207.
 (with ChangShou Lin and Chunyi Zhao)
Sharp estimates for fully bubbling solutions of a SU(3) Toda system
Geom. Funct. Anal. 22(2012), no.6, 15911635.
 (with CSLin and CY Zhao)
Asymptotic behavior of $SU(3)$ Toda system in a bounded domain
Manuscripta Math. 137(2012), no.12, 118.
 (with Monica Musso)
Nonradial solutions to critical elliptic equations of CaffarelliKohnNirenberg type
International Mathematics Research Notices.
18(2012), 41204162.
 (with Frank Pacard and M. Musso) Finiteenergy signchanging
solutions with dihedral symmetry for the stationary non linear
Schr\"{o}dinger equation Journal of European
Mathematical Society 14(2012), no.6, 19231953.
 (with A. Pakylak and F. Ting)
Multivortex solutions to GinzburgLandau equations with external potential
Archive Rational Mech. Analysis
204(2012), no.1, 314354.
 (with M. Winter)
FlowDistributed Spikes for Schnakenberg Kinetics
Journal of Mathematical Biology 64(2012), no.12, 211254.
 (with Jun Yang)
Vortex rings pinning for the GrossPitaevskii equation in three dimensional space
SIAM Journal of Mathematical Analysis 44(2012), no.6, 39914047.
 (with W. Yao)
Uniqueness of positive solutions to some coupled nonlinear Schr\"{o}dinger equations
CPAA
11(2012), no.3, 10031011
2011
 (with Weiwei Ao and M. Musso)
On Spikes Concentrating on LineSegments to a
Semilinear Neumann Problem
Journal of Differential Equations
251(2011), no.45, 881901.
 (with Weiwei Ao and M. Musso)
Triple Junction Solutions for a Singularly Perturbed Neumann Problem
SIAM Journal of Mathematical Analysis
43(2011), no.6, 25192541.
 (with D. Cao and I. Chern)
On ground states of spinor BoseEinstein condensates
NoDEA 18(2011), no.4, 427445.
 (with E.Dancer and S. Santra)
Least energy nodal solution of a singular perturbed problem with jumping
nonlinearity Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. (5) 10(2011), no.1, 1936.
 (with O. Druet and F. Robert)
The LinNi's problem for mean convex domains
Memoirs of American Mathematical Society
November 30, 2011
 (with Manuel del Pino)
Solutions to the AllenCahn Equation and Minimal Surfaces
Milan Journal of Mathematics
79(2011), 3965.
 (with M. del Pino and M. Kowalczyk)
On De Giorgi Conjecture in Dimensions $N \geq 9$ (final version)
Annals of Mathematics 174 (2011), no.3, 14851569.
 (with Yuxin Ge and Feng Zhou)
A critical elliptic problem for polyharmonic operators
J. Funct. Analysis 260(2011), no.8, 22472282.
 (with ZM Guo)
Global solution branch and Morse index estimates of a semilinear
elliptic equation with supercritical exponent
Trans. American Math. Soc.
363(2011), no.9, 47774799
 (with Z. Guo, Z. Liu F. Zhou)
Bifurcations of some elliptic problems with a singular
nonlinearity via Morse index
CPAA 10(2011), no.2, 507525.
 (with Meiyue Jiang and LP Wang)
$2\pi$periodic selfsimilar solutions for the anisotropic affine curve
shortening problem
Cal. Var. PDE 41(2011), no.34, 535565.
 (with Theodore Kolokolnikov)
Stability of spiky solutions in a competition model with crossdiffusion
SIAM Journal of Applied Mathematics
71(2011), no.4, 14281457.
 (with CS Lin and LP Wang)
Topological Degree For Solutions of A Fourth Order Mean Field Equation
Math. Zeit
268(2011), 675705.
 (with S. Santra)
Asymptotic behavior of solutions of a biharmonic Dirichlet problem with
large exponents
Journal d'Analyse Math. 115(2011), 131.
 (with L. Wang and S. Yan)
On LinNi's Conjecture in Convex Domains
Proc. London Math. Soc. 102(2011), 10991126.
 (with L. Wang and J. Yang)
On AmbrosettiMalchiodiNi Conjecture for General Hypersurfaces
Communications in Part. Diff. Eqns.
36(2011), vol. 12, 21172161
 (with L. Wei and F. Zhou)
Mixed interior and boundary nodal bubbling solutions for a sinhPoisson equation Pacific Journal of Mathematics 250(2011), no.1, 225256.
 (with W. Yao)
Asymptotic axisymmetry of the
subsonic traveling waves to the GrossPitaevskii equation
Comm. Contemp. Math.
13(2011), no.6, 10951104.
 (with S. Yan)
Infinitely many positive solutions for an elliptic problem with critical or supercritical growth
J. Math Pures Appl. (9) 96(2011), no.4, 307333.
 (with CY Zhao and F. Zhou)
On nondegeneracy of solutions of $SU(3)$ Toda system
CRAS 349(2011), no.34, 185190.
 (with EN Dancer and S. Santra)
Asymptotic behavior of the least energy solution of a problem with competing powers
Journal of Functional Analysis
261(2011), 675705.
2010
 (with H. Berestycki)
On Least Energy Solutions to A Semilinear Elliptic Equation in A Strip
DCDSA
28(2010), no.3, 10831099
 (with EN Dancer and T. Weth)
A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system
AIHP
27 (2010), pp. 953969
 (with Manuel del Pino and M. Kowalczyk)
The JacobiToda system and foliated interfaces
DCDSA
28(2010), no.3, 9751006.
 (with M. del Pino, M. Kowalczyk and F. Pacard)
The Toda system and multipleend solutions of autonomous planar elliptic problems
Advances in Mathematics
224(2010), no.4, 14621516.
 (with M. del Pino, M. Kowalczyk and F. Pacard)
Multipleend solutions to the AllenCahn equations in $R^2$
Journal of Functional Analaysis
258(2010), no.2, 458503.
 (with Manuel del Pino, M. Kowalczyk and Jun Yang)
Interface foliation near minimal submanifolds in Riemannian
manifolds with positive Ricci curvature
Geom. Funct. Anal. 20(2010), no.4, 918957.
 (with Qiang Du and C. Zhao)
Vortex Solutions of the High$\kappa$ Highfield GinzburgLandau
Model with an Applied Current
SIAM J. Math. Anal. 42(2010), no.6, 23682401.
 (with ZM Guo)
Qualitative properties of entire radial solutions for a biharmonic equation
with supcritical nonlinearity
Proc. American Math. Soc.
138(2010), no.11, 39573964.
 (with FH Lin)
Traveling Wave Solutions of Schr\"odinger Map Equation
Comm. Pure Appl. Math. 63(2010), no.12, 15851621.
 (with TC Lin and Xiaojin Chen) Blow up and solitary waves with
ring profiles for twocomponent nonlinear Schrodinger equations
Phys. D: Nonlinear Phenomena
239(2010), no.10, 613626.
 (with TC Lin and W. Yao)
Orbital stability of bound states of nonlinear
Schr\"{o}dinger equations with linear and nonlinear lattices
J. Diff. Eqns. 249(2010), no.9, 21112146.
 (with H. Tse and M. Winter)
The GiererMeinhardt System on a Compact
TwoDimensional Riemannian Manifold: Interaction of Gaussian Curvature and
Green's Function
J. Math. Pures Appl.
94(2010), no.4, 366397.
 (with Liping Wang and Shusen Yan)
A Neumann Problem with Critical Exponent in Nonconvex Domains and
LinNi's Conjecture
Transcation of Amer. Math. Soc.
362(2010), no.9, 45814615.
 (with M. Winter)
Stability of Spiky Solutions
in a ReactionDiffusion System with Four Morphogens
on the Real Line
SIAM J. Math. Anal. 42(2010), no.6, 28182841.
 (with S. Yan)
On an elliptic problem with critical growth
and a stronger LazerMcKenna conjecture
Ann. Scuola. Norm. Pisa
(5)9(2010), no.2, 423457.
 (with S. Yan)
Infinitely many positive solutions for the nonlinear Schr\"odinger equations
in $ R^N$ Cal.Var. PDE
37(2010), 423439.
 (with Shusen Yan)
Infinitely many solutions for the prescribed scalar curvature
problem on $\Sn^N$
Journal Functional Analysis
258(2010), 30483081.
 (with Jun Yang)
Toda system and cluster phase transition layers in an inhomogeneous phase
transition model
Asymptotic Analysis
69(2010), no.34, 175218.
 (with Dong Ye)
On MEMS equations with fringing fields
Proc. American Math. Soc.
138(2010), no.5, 16931699.
2009
 (with E.N. Dancer)
Spike Solutions in coupled nonlinear Schr\"odinger equations with
Attractive Interaction
Transc. American Math. Soc. 361(2009), no.3, 11891208.
 (with P. Esposito)
Nonsimple Blowup Solutions for the Neumann twodimensional $\sinh$Gordon equation
Cal Var. PDE 34(2009), no.3, 341375.
 (with YX Guo)
Supercritical biharmonic elliptic problems in domains with small holes
Math. Nach. 282(2009), no.12, 17241739.
 (with D. Iron, T. Kolokolonikov, J. Rumsey )
Stability of curved interfaces in the perturbed twodimensional AllenCahn system
SIAM Journal of Applied Math.
69(2009), no.5, 12281243.
 (with Theodore Kolokolnikov and M. Ward)
Spot selfreplication and dynamics for the Schnakenburg model in a twodimensional domain
Journal of Nonlinear Science 19(2009), no.1, 156.
 (with T. Kolokolnikov and M. Winter)
Existence and Stability Analysis of
Spiky Solutions for the GiererMeinhardt System with Large Reaction Rates
Physica D: Nonlinear Phenomena
238(2009), no.16, 16951710.
 (with Fanghua Lin and Taichia Lin)
Skymions in GrossPitaevskii Functionals
Acta Mathematica Scientia
2009, 29B(3): 751776. Special Volume dedicated to Prof. Wu Wenjun's 90th birthday.
 (with PK Maini and M. Winter)
Stability of Spikes in the Shadow GiererMeinhardt system with
Robin Boundary Conditions
Chaos (special issue on pattern formations in reactiondiffusion systems)
17(2009),037106, 16pp. .
 (with X.Ren)
On a phase field problem driven by interface tension and interface curvature
Eur.J. Appl.Math.
20(2009), no.6, 531556.
 (with X. Ren)
Oval shaped droplet solutions in the saturation process of some pattern formation problems
SIAM Journal of Applied Mathematics
70(2009), no.4, 11201138.
 (with S.Santra)
Homoclinic solutions for fourth order travelling wave equations
SIAM J. Math. Anal.
41(2009), no.5, 20382056.
 (with M. Winter)
Spikes for the GiererMeinhardt system with discontinuous diffusion coefficients
Journal of Nonlinear Science
19(2009), no.3, 301339.
 (with M. Winter)
Strongly Interacting Bumps for the SchrodingerNewton Equations
Journal of Mathematical Physics
50(2009), no.1, 012905.
 (with M. Winter)
On the GiererMeinhardt system with precursors
DCDSA, special issue for Prof. Mimura's 65th Birthday
25(2009), no.1, 363398.
 (with Xingwang Xu)
Prescribing $Q$curvature problem on $S^n$
Journal of Functional Analaysis
257(2009), no.7, 19952023.
 (with J. Yang)
Solutions with transition layer and spike in an inhomogeneous phase transition model
Journal of Differential Equations
246(2009), no.9, 36423667.
2008
 (with C. Bandle)
Multiple Clustered Layer Solutions for Semilinear Elliptic Problems on $S^n$
Comm. Partial Diff. Equations 33(2008), no.46, 613635.
 (with Juan D\'avila, Manuel del Pino and Monica Musso)
Fast and slow decay solutions for supercritical elliptic
problems in exterior domains
Calculus of Variations and PDE 32(2008), no.4, 765786.
 (with Manuel del Pino and Mike Kowalczyk )
The Toda system and clustering interfaces in the AllenCahn
equation
Archive Rational Mechanical Analysis 190(2008), no.1, 141187.
 (with M. del Pino and M. Kowalczyk)
On De Giorgi Conjecture in Large Dimensions
C. R. A. S.
346(2008), no.2324, 12611266.
 (with Y. Ding)
Stationary states of nonlinear Dirac equations with general
potentials
Reviews in Mathemmatical Physics 20(2008), no.8, 10071032.
 (with ZM Guo)
Asymptotic Behavior of touchdown solutions and global bifurcations
for an elliptic problem with a singular nonlinearity
Comm. Pure Appl. Anal.
7(2008), no.4, 765786.
 (with ZM Guo)
Infinitely many turning points for an elliptic problem with a
singular nonlinearity
Journal of London Mathematical Society, 78(2008), no.1, 2135.
 (with Z.M. Guo)
Entire solutions and global bifurcations for a biharmonic equation with singular nonlinearity in $\mathbb R^3$
Adv. Diff. Eqns. 13(2008), no.78, 743780.
 (with ZM Guo)
On a fourth order elliptic problem with negative exponent
SIAM J. Math. Anal.
40(2008/09), no.5, 20342054.
 (with ZM Guo)
On solutions with point ruptures for a semilinear Elliptic
problem with singularity
Methods of Analysis and Applications, special issue on MEMS 15(2008), no.3, 377390.
 (with YX Guo)
Nonexistence of positive finite Morse index solutions to an elliptic problem with singular nonlinearity
Methods of Analysis and Applications, special issue on MEMS 15(2008), no.3, 377390.
 (with Theodore Kolokolnikov)
Positive Clustered Layered Solutions For the GiererMeinhardt System
Journal of Differential Equations 245(2008), no.4, 964993.
 (with TC Lin)
Orbital stability of bound states of semiclassical nonlinear
Schr\"{o}dinger equations with critical nonlinearity
SIAM J. Mathematical Analysis 40(2008), no.1, 365381.
 (with Li Ma)
Properties of positive solutions to an Elliptic Equation with
negative exponent
Journal of Functional Analysis 254(2008), no.4, 10581087.
 (with F.Mahmoudi and A. Malchiodi)
Transition Layer for the Heterogeneous AllenCahn Equation
Ann. Non linearie, Annoles de l'Institut H. Poincare, 25(2008), no.3, 609631.
 (with X. Ren)
The critical mass constraint in the CahnHilliard equation
Interfaces and Free Boundary Problems 10(2008), no.3, 301338.
 (with X. Ren)
Spherical solutions to a free boundary problem from diblock copolymer morphology
SIAM Journal of Mathematical Analysis 39(2008), no.5, 14971535.
 (with F. Robert)
Asymptotic behavior of a fourth order equation with Dirichlet boundary condition
Indiana Univ. Math. J. 57(2008), no.5, 20392060.
 (with Wang Hung Tse and M. Winter)
Spikes for the GiererMeinhardt System with Many Segments of
Different Diffusivities
Bulletin of Academia Sinica (New Series), Special volume in celebration of Prof. M. Mimura's 65th birthday
3(2008), no.4, 525566.
 (with Liping Wang)
Solutions with Interior Bubble and Boundary Layer for an Elliptic
Problem
DCDSA (special volume in celebration of Dancer's sixtieth birthday) 21(2008), no.1, 333351.
 (with Tobias Weth )
Radial solutions and phase separation in a system of two coupled Schr\"odinger equations,
Archive Rational Mechanical Analysis 190(2008), no.1, 83106.
 (with T. Weth)
Asymptotic behavior of solutions of planar elliptic
systems with strong competition
Nonlinearity 21(2008), no.2, 305317.
 (with M. Winter)
Stationary Multiple Spots for ReactionDiffusion Systems
Journal of Mathematical Biology 57(2008), no.1, 5389.
 (with M. Winter)
Mutually Exclusive Spiky Pattern and Segmentation Modeled by the
FiveComponent MeinhardtGierer System
SIAM J. Appl. Math. 69(2008), no.2, 419452.
 (with Jun Yang)
Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain
DCDSA 22(2008), no.3, 465508.
 (with Dong Ye)
Nonradial solutions for a conformally invariant fourth order equation in $R^4$
Cal. Var. PDE 32(2008), no.3, 373386.
 (with F. Zhou and Dong Ye)
Analysis of boundary bubbling solutions for an anisotropic Emden
Fowler equation, Ann. Non linearie, Annoles de l'Institut H. Poincare, 25(2008), no.3, 425447.
2007
 (with C. Bandle)
Nonradial Clustered Spike Solutions for Semilinear Elliptic Problems
on $S^n$ J' Analyse Math. 102(2007), 181208.
 (with T. Bartsch and Zhiqiang Wang)
Bound states for a coupled nonlinear Schrodinger system
JFPTA 2(2007), no.2, 353367.
 (with E.Dancer)
Signchanging solutions for supercritical elliptic problems in domains with small holes
Manuscripta Mathematica 123(2007), no.4, 493511.
 (with D'Aprile) Clustered Solutions Around Harmonic Centers to a Coupled
Elliptic System . Ann. Non linearie, Annoles de l'Institut H. Poincare, 24(2007), no.4, 605628
 (with Juan D\'avila, Manuel del Pino and M. Musso)
Standing waves for supercritical nonlinear Schr\"odinger
equations
. Journal of Differential Equations 236(2007), no.1, 164198.
 (with M. del Pino and M. Kowalczyk)
Concentration on curves for
nonlinear Schr\"odinger equations
Communications on Pure and Applied Mathematics 60 (2007), no. 1, 113146.
 (with M. del Pino) Supercritical elliptic problems in domains with small holes . Ann. Non linearie, Annoles de l'Institut H. Poincare, 24(2007), no.4, 507520.
 (with YH Ding)
Semiclassical states for nonlinear Schrodinger equations with signchanging potentials Journal of Functional Analysis 251(2007), no.2, 546572.
 (with Th. Kolokolnikov and Michael Ward )
Selfreplication of mesa patterns in reactiondiffusion systems,
Physica D: Nonlinear Phenomena 236(2007), no.2, 104122.

(with Z. Guo)
Symmetry of Nonnegative Solutions of a Semilinear
Elliptic Equation with Singular Nonlinearity
. Proc. Royal. Soc. Edinburgh.
Section A. (Mathematics) 137(2007), no.5, 963994.
 (with Guo ZM)
On the Cauchy problem for a reactiondiffusion equation
with a singular nonlinearity
J. Diff. Eqns. 240(2007), 181208.
 (with F.H. Lin and W.M. Ni) On the Number of Interior Peak Solutions for A Singularly Perturbed Neumann Problem Communications on Pure and Applied Mathematics 60 (2007), no. 2, 252281.
 (with C.S. Lin) Uniqueness of multiplespike solutions via the Method of Moving Planes Pure and Applied Mathematics, A Quarterly Journal (special volume in honour of L. Simon's 60th birthday), 3(2007), no.2, part 2, 689735.
 (with CS Lin)
Sharp Estimates For Bubbling Solutions of A Fourth Order Mean Field Equation
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, (5)6(2007), no.4, 599630.
 (with CS Lin and L. Wang)
Bubble Accumulations In An Elliptic Neumann Problem With Critical Sobolev Exponent
. Cal. Var. PDE 30(2007),no.2, 153182.
 (with TCLin)
HalfSkyrmions and SpikeVortex Solutions of Twocomponent Nonlinear Schr\"{o}dinger Systems
. Journal of Mathematical Physics 48(2007), no.5, 053518.
 (with A. Malchiodi)
Boundary Interface for the AllenCahn Equation
Journal of Fixed Point Theory and Applications (JFPTA) 1(2007), no.2, 305336.
 (with A. Malchiodi and W.M. Ni) Boundary Clustered Interfaces for Allen Cahn Equation
. Pacific Journal of Mathematics , 229(2007), no.2, 447468.
 (with J. Norbury and M. Winter)
Stability of patterns with arbitrary period
for a GinzburgLandau equation with a mean
field . European Journal of Applied Mathematics 18(2007), no.2, 129151.
 (with Xiaofeng Ren)
Single droplet pattern in the cylindrical phase of
diblock copolymer morphology
Journal of Nonlinear Science 17(2007), no.5, 471503
 (with X. Ren)
Many droplet pattern in the cylindrical phase of
diblock copolymer morphology
Reviews in Mathematical Physics 19(2007), no.8, 879921.
 (with M. Winter)
Symmetric and asymmetric clusters in an elliptic system. NoDEA, 14(2007), no.56, 787823.
 (with M. Winter)
Existence, Classification and Stability Analysis of Multiplepeaked Solutions
for the GiererMeinhardt System in $R^1$
Methods Appl. Anal. 14(2007), no.2, 119163.
 (with Tobias Weth )
Nonradial Symmetric Bound States for a System of Coupled Schr\"odinger
Equations
Rendiconti Lincei:Matematica e Applicazioni 18(2007), no.3, 279293.
 (with S. Yan) Arbitrary many boundary peak solutions for An Elliptic Neumann problem
with critical growth
J. Math. Pures Appl. (9)88(2007), no.4, 350378.
 (with S. Yan)
LazerMckenna conjecture: the critical case . Journal of Functional Analysis 244(2007), 639667.
 (with S. Yan)
New Solutions For Nonlinear Schr\"odinger Equations with critical
nonlinearity
. Journal of Differential Equations 237(2007), no.2, 446472.
 (with Jun Yang)
Concentration on Lines for a Singularly Perturbed Neumann Problem
in TwoDimensional Domains , Indiana Univ. Math. Journal, 56(2007), no.6, 30253073.
 (with D. Ye and F. Zhou)
Bubbling Solutions for an Anisotropic EmdenFowler Equation
Cal. Var. and Part. Diff. Eqns. 28(2007), 217247.
2006
 (with T. D'Aprile) Standing waves in the MaxwellSchrodinger qquation and an optimal configuration problem. Cal. Var. and PDE, 25(2006), 105137.
 (with D'Aprile)
Layered solutions for a semilinear elliptic system in a ball
J. Diff. Eqns. 226(2006), 269294.
 (with T. D'Aprile) Boundary Concentration in radial solutions for a system of semilinear elliptic equations Journal of London Mathematical Society 74(2006), no.2, 415440.

(with D'Aprile)
Locating the boundary peaks of leastenergy solutions to a
singularly perturbed Dirichlet problem
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Vol. V (2006), 219259.
 (with Juan D\'avila, Manuel del Pino, Monica Musso )
Singular limits of a twodimensional boundary value problem
arising in corrosion modelling
Archive Rational Mechanical Analysis 182(2006), no.2, 181221.
 (with M. del Pino)
Collapsing steady states of the KellerSegel system
Nonlinearity 19(2006), no.3, 661684.
 (with M. del Pino and M. Kowalczyk)
Resonance and interior layers in an inhomogeneous phase
transition model . SIAM J. Math. Anal., 38(2006), no.5, 15421564.
 (with P. Esposita and A. Pistoia)
Concentrating solutions for Henon equation in R^2
J' Analyse Math. 100(2006), 249280.
 (with T. Kolokolnikov and M. J. Ward) Zigzag and breakup instabilities of stripes and rings for the twodimensional GrayScott model. Studies in Applied Math. 116(2006), no.1, 3595.
 (with T. Kolokolnikov, Thomas Erneux)
Mesatype patterns in the onedimensional Brusselator and their stability
Physica D: Nonlinear Phenomena 214(2006), no.1, 6377.
 (with T. Kolokolnikov, M. Ward)
Slow translational instabilities of spike patterns in the onedimensional GrayScott model
Interfaces and Free Boundaries 8(2006), no.2, 185222.
 (with T. Kolokolnikov, M. Ward)
The Stability of A Stripe for the GiererMeinhardt Model and the
Effect of Saturation SIAM J. Applied. Dynamical Systems 5(2006), no.2, 313363.
 (with ZM Guo)
Hausdorff Dimension of Ruptures for Solutions of a Semilinear
Elliptic Equation with Singular Nonlinearity
Manuscripta Mathematica 120(2006), 193209.
 (with T.C. Lin)
Spikes in Twocomponent Systems of Nonlinear
Schr\"{o}dinger Equations with Trapping Potentials
Journal of Differential Equations 229(2006), no.2, 538569.
 (with TC Lin) Solitary and Selfsimilar Solutions of Twocomponent
System of Nonlinear Schr\"{o}dinger Equations . Physica D: Nonlinear Phenomena 220(2006), no. 2, 99115
 (with TC Lin)
Symbiotic bright solitary wave solutions of coupled nonlinear
Schroedinger equations . Nonlinearity 19(2006), no.12, 27552773.
 (with M. Musso) Stationary Solutions to a KellerSegel Chemotaxis System Asymptotic Analysis, 49(2006), no.34, 217247.,
 (with W.M. Ni) On positive solutions concentrating on spheres for the GiererMeinhardt system J. Diff. Eqns. 221(2006), 158189.
 (with X. Ren)
Droplet Solutions in the Diblock Copolymer Problem with Skewed
Monomer Composition Cal. Var. and Part. Diff. Eqns. 25(2006), no.3, 333359.
 (with Xiaofeng Ren)
Existence and Stability of Spherically Layered
Solutions of the Diblock Copolymer Equation
SIAM J. Appl. Math. 66(2006), 10801099.
 (with M. Winter)
Standing waves in the FitzHughNagumo system and a problem in combinatorial geometry
Math. Zeit 254(2006), no.2, 359383.

(with S. Yan) Solution Explosant Au Centre Et Le Long Du Bord Pour Un Probl\`{e}me Elliptique
De Neumann Avec NonLin\'{e}arit\'e Critique . C. R. Acad. Sci. Paris, 343(2006), no.5, 311316.
 (with D. Ye and F. Zhou)
Bubbling Solutions for an Anisotropic EmdenFowler Equation
Comp. Rend. Acad. Sci. Paris 343(2006), no.4, 253258.
2005
 (with Wenyi Chen)
On BrezisNirenberg Problem on $\Sn^3$ and A Conjecture of BandleBenguria
Com. Rend. Acad. Sci. Paris 341(2005), no.3, 153156.
 (with M. del Pino and M. Kowalczyk)
Nonlinear Schr\"odinger equations:
Concentration on weighted geodesics in the semiclassical limit
Comp. Rend. Acad. Sci. Paris 341(2005), no. 4, 223228.
 (with T. D'Aprile) On bound states
concentrating on spheres for the MaxwellSchrodinger Equation SIAM J. Math. Anal. 37(2005), no. 1, 321342.
 (with Theo Kolokolnikov)
On ringlike solutions for the GrayScott model: existence, instability
and selfreplicating rings Eur. J. Appl. Math., 16(2005), no.2, 201237.
 (with Theo Kolokolnikov and M.J.Ward)
Pulsesplitting for some reactiondiffusion systems in onespace dimension,
Studies in Appl. Math. 114(2005), no.2, 115165.
 (with Theo Kolokolnikov and M. Ward)
The existence and stability of spike equilibria in the onedimensional GrayScott model: the pulsesplitting regime. Physica D: Nonlinear Phenomenon 202(2005), 258293.
 (with Theo Kolokolnikov and M.J.Ward)
The existence and stability of spike equilibria in the onedimensional GrayScott model, Appl. Math. Letters, 18(2005), no. 8, 951956.
 (with Theo Kolokolnikov and M. Ward)
The existence and stability of spike equilibria in the onedimensional GrayScott model: the low feedrate regime. Studies in Appl. Math. 115(2005), no.1, 2171.
 (with M.E. Hubbard and J. A. Leach) Pattern formation
in a twodimensional simple chemical system with general orders of autocatalysis and decay. IMA J. Appl. Math., 70(6)(2005), 723747.
 (with T.C. Lin) Spikes in two coupled nonlinear Schrodinger equations . Ann. Non linearie, Annoles de l'Institut H. Poincare, 22(2005), no. 4, 403439.
 (with T.C. Lin) Ground state of $N$ coupled Nonlinear Schr\"{o}dinger Equations in $R^n, n\leq 3$ Communications in Mathematical Physics 255(3)(2005), 629653.
 (with W.M. Ni and A. Malchiodi) Multiple clustered layer solutions for semilinear Neumann problems on
a ball, Ann. Non linearie, Annoles de l'Institut H. Poincare 22(2005), 143163.
 (with O. Rey) Blowing up Solutions for an Elliptic Neumann Problem with Sub or Supercritical Nonlinearity. Part II: $N \geq 4$, Ann. Non linearie, Annoles de l'Institut H. Poincare, 22(2005), no. 4, 459484.
 (with O. Rey)
Arbitrary Number of Positive Solutions For an Elliptic Problem with Critical Nonlinearity. Journal of European Mathematical Society 7(2005), no. 4, 449476.
 (with X. Ren) Wriggled lamellar solutions and their stability
in the Diblock copolymer problem , SIAM J. Math. Anal. 37(2005), no.2, 455489.
 (with Xiaofeng Ren) Nucleation in the FitzHughNagumo System: InterfaceSpike Solutions Journal of Differential Equations 205(2005), 266301.
 (with B.D. Sleeman and M.J.Ward)
The existence, stability, and dynamics of spike patterns in a chemotaxsis model , SIAM J. Appl. Math., 65(2005), no. 3, 790817.
 (with Tobias Weth) On the Number of Nodal Solutions to a Singularly Perturbed Neumann
Problem Manuscripta Mathematica 117(2005), no. 3, 333344.
 (with M. Winter)
On a cubicquintic GinzburgLandau equation with global coupling, Proceedings of Amer. Math. Soc. 133(2005), no. 6, 17871796.
 (with Matthias Winter) Clustered spots in the FitzHughNagumo system Journal of Differential Equations, 213(2005), no.1, 121145.
 (with M. Winter)
Symmetry of nodal solutions for singularly perturbed elliptic problems on a ball, Indiana Univ. Math. Journal, 54(2005), no. 3, 707741.
 (with M. Winter and W.K. Yeung) A higherorder energy expansion to twodimensional singularly
perturbed Neumann problems Asymptotic Analysis, 43(2005), no.12, 75110.
 (with Xingwang Xu)
Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in $R^3$
Pacific J. Math., 221(2005), no.1, 159165.
2004
 (with D. Iron and M. Winter)
Stability analysis of Turing patterns generated by the Schnakenberg
model Journal of Math. Biology 49(2004), no.4, 358390.
 (with O. Rey) Blowing up solutions for an elliptic Neumann
problem with sub or supercritical nonlinearity I: $N=3$,
Journal of Functional Analysis 212(2004), no.2, 472499.
 (with X. Ren) Molecular chirality and solitonstripe pattern in liquid crystal films Nonlinearity 17(2004), Vol. 2, 617632.
 (with X. Ren) The solitonstripe pattern in the SeulAndelman membrane Physica D:Nonlinear Phenomenon 188 (2004), no. 34, 277291.
 (with X. Ren) Stability of spot and ring solutions of the
Diblock copolymer equation Journal of Mathematical Physics 45(2004), no.11, 41064133.
 (with M. Winter)
Asymmetric Patterns for the GiererMeinhardt system J. Math. Pures Appl. (9)83(2004), no.4, 433476.
 (with M. Winter)
On GiererMeinhardt system with saturation Comm. Contemp. Math. 6(2004), no.2, 259277.
 (with M. Winter)
Higher order expansions and spike locations Cal. Var. PDE
20(2004), 403430.
2003
 (with H. Berestycki) On singular perturbation problems with Robin boundary condition, Annali Suola Norm. Sup. Pisa Cl.Sci. (5) Vol.II (2003), 199230.
 (with del Pino and M. Kowalczyk)
Multibump Ground States of the GiererMeinhardt system in
$R^2$, Ann. Non linearie, Annoles de l'Institut H. Poincare 20(2003), 5385.
 (with J. Leach) Pattern
formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis. Physica D:Nonlinear Phenomena 34(180)2003, 185209.
 (with C.S. Lin) Locating the peaks of solutions via the Maximum Principle II: A local version of the method of moving planes. Comm. Pure Appl. Math. 6(2003), 784809.
 (with X. Ren) Triblock copolymer theory: ordered ABC lamellar phase. Journal of Nonlinear Sciences 13(2003), 175208.
 (with X. Ren) Triblock copolymer theory: free energy, disordered phase and weak segregation, Physica D:Nonlinear Phenomena 178(2003), 103117.
 (with X. Ren) On energy minimizers
of the diblock copolymer problem. Interfaces and Free Boundaries 5 (2003), no. 2, 193238.
 (with X. Ren)
On the spectra of 3D Lamellar solutions of the Diblock copolymer problem SIAM J. Math. Anal. 35(1)(2003), 132.
 (with X. Ren) Solitonstripe patterns in the charged
Langmuir monolayers Journal of Nonlinear Sciences 13 (2003), no. 6, 603624.
 (with X. Sun, T. Tang and M. Ward)
Numerical challenges for resolving spike dynamics for two
onedimensional reactiondiffusion systems, Studies in Appl. Math. 111 (1)(2003), 4184.
 (with M.J.Ward)
Hopf bifurcations and oscillatory instabilities of spike solutions for the onedimensional GiererMeinhardt model. Journal of Nonlinear Sciences 13(2003), 209264.
 (with M.J.Ward)
Hopf bifurcations of spike solutions for the shadow GiererMeinhardt model Europ. J. Appl. Math. 14 (2003), 677711.
 (with M. Winter)
Asymmetric spotty patterns for the GrayScott model, Studies in Appl. Math. 110(2003), 63102.
 (with M. Winter)
A nonloal eigenvalue problem and the
stability of spikes for reactiondiffusion systems with fractional
reaction rates, Int. J. Bifur. Chaos 13 (6) (2003), 15291543.
 (with M. Winter)
Existence and stability of multiple spot solutions for the GrayScott model in $R^2$, Physica D: Nonlinear Phenomena 176(2003), 147180.
 (with M. Winter) Higher order energy expansions for some singularly perturbed Neumann problems, Comptes Rend de L' Acad. des Sci. I. Math. 337(2003), 3742.
 (with M. Winter) Stability of monotone solutions for the shadow GiererMeinhardt system with finite diffusivity, Diff. Int. Eqns. 16(2003), 11531180.
2002
 (with Guofang Wang) Steady State Solutions Of A ReactionDiffusion System Modeling Chemotaxis, Math. Nach. 233234(2002), 221236..
 (with Guofang Wang) On a conjecture of Wolansky, Nonlinear Analysis:TMA 48(2002), 927937.
 (with S.I. Ei) Dynamics of metastable localized patterns and
its application to the interaction of spike solutions
for the GiererMeinhardt systems in two spatial dimension, Japan J.
Industr. Appl. Math. 19(2002), 181226
 (with J. Norbury and M. Winter)
Existence and stability of singular patterns
in a GinzburgLandau equation coupled with a mean field, Nonlinearity 15(2002), 20772096.
 (with X. Ren) Concentrically layered energy equilibria of the diblock copolymer problem, Europ. J. Appl. Math. 13(2002), 479496.
 (with M. Ward)
Asymmetric Spike Patterns for the Onedimensional GiererMeinhardt System: Equilibria and Stability, Europ. J. Appl. Math. 13(2002), 283320.
 (with M.J. Ward ) The existence and stability of asymmetric spike patterns for the Schnakenberg
model, Studies in Appl. Math. 109(2002), 229264.
 (with M. Winter) Spikes for
the TwoDimensional GiererMeinhardt System: The Strong Coupl
ing Case, J. Diff. Eqns. 178(2002), 478518.
 (with M. Winter) Critical threshold and stability of cluster
solutions for large reactiondiffusion systems in $R^1$,
SIAM J. Math. Anal. 33(2002), 10581089.
2001
 Pattern formations in twodimensional GrayScott model: existence of singlespot solutions and their stability, Physica D: Nonlinear Phenomena 148(2001), 12, 2048.
 Uniqueness and critical spectrum of boundary
spike solutions, Proc. Royal Soc. Edin. A 131(2001), 14571480.

Multiple condensations for a nonlinear elliptic equation with
subcritical growth and critical behavior, Proc. Edinburgh Math.
Soc. 44(2001), 631660.
 (with J. Ai and K.S. Chou) Selfsimilar solutions for
the anisotropic affine curvature shortening problem, Cal. Var. PDE
13 (2001), 311337.
 (with D. Iron and M.J. Ward) The stability of spike solutions to the onedimensional GiererMeinhardt model, Physica D.: Nonlinear Phenomena 150 (2001), no. 12, 2562.
 (with G. Lu and X. Xu) On Conformally Invariant Equation $ (\Delta u)^p uK(x)u^{\frac{N+2p}{N2p}}=0$ and Its Generalizations, Annali di Mathematica Pura ed Applicata 179(2001), 309329.
 (with L. Ma) Convergence for a Liouville equation, Comment. Math. Helv. 76(2001), 506514.
 (with M. Winter)Solutions for the CahnHilliard equation with many boundary spike layers,
Proc. Roy Soc Edinb A 131(2001), 185204.
 (with M. Winter) Spikes for the
TwoDimensional GiererMeinhardt System: The Weak Coupling Case
Journal of Nonlinear Sciences 6(2001), 415458.
 (with M. Winter) On a Hypercycle System with Nonlinear Rate, Methods Appl. Anal. 8(2001), 257278.

(with L. Zhang) On a nonlocal eigenvalue problem, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, XXX (2001), 4162.
2000
 On the effect of the domain geometry in a singularly perturb
ed Dirichlet problem, Diff. Int. Eqns 13(2000), 1545.

On a nonlocal eigenvalue problem and its applications to pointcondensations in reactiondiffusion systems, Int. J. Bifurcation and Chaos, Vol. 10 (6) (2000), 14851496.

(with M. del Pino and Felmer )
On the role of distance function in some singular perturbation pr
oblems,
Comm. PDE 25(2000), 155177.

(with M. Del Pino and P. Felmer ) Mutiple peak solutions for some singular perturbation problems,
Cal. Var. PDE. 10(2000), 119134.
 (with M. Grossi, A. Pistoia) Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Cal. Var. & PDE 11(2000) 143175.

(with C. Gui)
On a sharp MoserAubinOnofri inequality for functions on $S^2
$ with symmetry, Pacific J. Math. 194(2000), 349358.

(with Gui and M. Winter) Mutiple boundary peak solutions for some singularly perturbed Neumann problems,
Ann. Non linearie, Annoles de l'Institut H. Poincare,
, 17(2000), 4782.
 (with C. Gui) On multiple mixed
interior and boundary peak solutions for some singularly
perturbed Neumann problems, Can. J. Math. 52(2000), 522538.
 (with Xiaosong Kang)
On interacting bumps of
semiclassical states of nonlinear Schr\"odinger equations,
Adv. Diff. Eqns. Vol. 5 (2000), 899928.
 (with G. Lu)On a Sobolev inequality with remainder terms, Proceedings of AMS
128(2000), 7584.

(with Xiaofeng Ren) On the
multiplicity of solutions of two nonlocal variational problems, SIAM J. Math. Anal. 31(2000), 909924.
 (with M. Winter) MultiInteriorSpike solutions
for the CahnHilliard equation with arbitrarily many peaks, Cal. Var. PDE 10(2000), 249289.
 (with M. Winter) On a two dimensional reactiondiffusion system with hypercyclical structure, Nonlinearity 13(2000), 20052032.
1999
 Point condensations of a model for fungal development,
C. R. Acad. Sci. Paris 328(1999), 129134.
 Existence, stability and metastability of point condensation patterns generated by GrayScott System Nonlinearity 12(1999), 593616.
 On single interior spike solutions of GiererMeinhardt system: uniqueness,
spectrum estimates,
Europ. J. Appl. Math. 10(1999), 353378.
 (with E.N.Dancer) On the location
of spikes and profile of solutions with two sharp layers, J. Diff. Eqns. 157(1999), 82101.
 (with M. del Pino and Felmer )
On the role of mean curvature in some singularly perturbed
Neumann problems, SIAM J. Math. Anal. 31 (1999), 6379.
 (with C. Gui)
Mutiple interior peak solutions for some singularly perturbed Neumann problems,
J. Diff. Eqns. 158(1999), 127.
 (with Xuefeng Wang) Shift and stability of ground states of a nonlinear Schr\"odinger equation outside
a small insulated domain, J. Diff. Eqns. 154(1999), 7395.
 (with Winter) Multiplepeak solutions for a wide class of sing
ular perturbation problems, J. London Math. Soc. 59(2)(1999), 585606.
 (with M. Winter)
On the two dimensional GiererMeinhardt system with strong coupling,
SIAM J. Math. Anal. 30(1999), 12411243.
 (with Xingwang Xu)
Classification of solutions of high order conformally invariant equations,
Math. Annalen 313(2)(1999), 207228.
1998
 Asymptotic behavior of leastenergy solutions of a semilinear
Dirichlet problem involving critical Sobolev exponent, J. Math. Soc.
of Japan , Vol 1 (1998), 139153.
 On the interior spike layer solutions of a singularly perturbed
semilinear Neumann problem, Tohoku Math. J. , Vol. 50 (2), 1998, 159178.
 Conditions for twopeaked solutions of singularly perturbed elliptic equations,
Manuscripta Mathematica , 96(1998), 113136.
 On the interior spike layer solutions for some singular perturbation problems, Proc. Royal
Soc. Edinburgh, Section A (Mathematics) , 128 (1998), 849874.
 (with G. Cerami) Multiplicity of multiple interior spike solutions for some singularly perturbed Neumann problem,
International Mathematics Research Notes , 12(1998), 601626.
 (with E.N.Dancer) On the effect of domain topology in some singular perturbation problems,
Topological Methods in Nonlinear Analysis 11(2) (1998), 227248.
 (with M. Flucher) Asymptotic behavior of elliptic free boundary
problem, Math. Zeit 228(1998), 683703.
 (with G. Lu) On Nonlinear Schrodinger Equations With Totally Degenerate Potentials,
C. R. Acad. Sci. Paris, , 326(1998), 691696.
 (with E. Noussair ) On the existence and profile of nodal solutions of some singularly perturbed
semilinear Neumann problem, Comm. Partial Diff. Eqns. , 23(1998), 793816.
 (with W.M. Ni and I. Takagi) On the location and profile of sp
ikelayer solutions to singularly perturbed semilinear Dirichlet problems:
intermediate solutions, Duke Math. J. 94 (1998), 597618.
 (with M. Winter ) Stationary solutions of CahnHilliard equation,
Ann. Non linearie, Annoles de l'Institut H. Poincare 15 (1998), 459492.
 (with M. Winter ) On the CahnHilliard equations II: interior spike Layer solutions,
J. Diff. Eqns. 148(1998), 231267.
 (with M. Winter) On the stationary CahnHilliard equation:
Bubble solutions, SIAM Journal on Mathematical Analysis 29(1998), 14921518.
 (with Xingwang Xu) On Conformal Deformations of Metrics On $S^n$
J. Functional Analysis , 157(1998), 292325.
1997
 On the boundary spike layer solutions of a singularly perturbed
semilinear Neumann problem, J. Diff. Eqns, 134 (1997), 104133.
 Exact Multiplicity for Some Nonlinear Elliptic Equations in Balls,
Proc. Amer. Math. Soc., 125 (1997), No. 11, 32353242.
 (with Dancer) On the profile of solutions with two sharp layers
to a singularly perturbed semilinear Dirichlet problem, Proc. Royal
Soc. Edinburgh, Section A (Mathematics), 127 A(1997), 691701.
 (with M. Flucher) Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots,
Manuscript. Math. 94 (1997), 337346.
 (with G. Lu) On positive entire solutions to the Yamabetype problem on
the Heisenberg and stratified groups, Electronic Research Announcements of American Mathematical Society
, 3(1997), 8389.
 (with E. Noussair ) On the effect of domain geometry on the exist
ence and profile of nodal solutions of some singularly perturbed semilinear Dirichlet problem,
Indiana Univ. Math. J. , 46(1997), 12551272.
1996
 On construction of singlepeak spiky solutions
to singularly perturbed semilinear Dirichlet problems, J. Diff. Eqns.
129 (2) 1996, 315333.
 Asymptotic behavior of a nonlinear fourth order eigenvalue problem, Comm. Part. Diff. Eqns. , 21 (1996), 14511468.
 (with X. Ren) Singlepoint condensation and least energy solutions,
Proc. Amer. Math. Soc, 124 (1) 1996, 111120.
1995
 (with W.M. Ni) On the location and profile of spikelayer
solutions to singularly perturbed semilinear Dirichlet problems,
Comm. Pure Appl. Math. , 48(1995), 723761.
 (with X. Ren) Counting peaks of solutions to some quasilinear
elliptic equations with large exponent,
J. Diff. Eqn., 117(1995), 2855.
 (with X. Ren) Asymptotic behavior of least energy solutions to
a two dimensional semilinear problem with mixed boundary condition,
Nonlinear Analysis: Theory, Methods and Applications, 24(4) 1995, 5876
04.
 (with X. Ren) On a semilinear equation in $R^{2}$ when the exponent approaches infinity,
J. Math. Anal. Appl., 189(1995), 179193.
 (with X. Wang) On the equation
$ \Delta u + K(x) u^{\frac{n+2}{n2} \pm \epsilon^{2}}=0$ in
$ R^{n} $, Rendiconti Del Circolo Matematico Di Palermo , XLIV (1995), 137.
1994
 (with X. Ren) On a two dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc. , 343 (2) 1994, 749763.
Publications in Proceedings of Conference as Invited Talks:
 On the effect of domain geometry and boundary geometry in some singular perturbation problems, Differential Equations and Applications (P. Bates ed.) , International Press, 1998,326339.
 On the construction of interior spike layer solutions to a singularly perturbed semilinear Neumann problem,
PARTIAL DIFFERENTIAL EQUATIONS:THEORY AND NUMERICAL SOLUTION ,
CRC Press LLC, 1998, 336349.
 Existence and Stability of Spikes for the GiererMeinhardt System (99 Pages) HANDBOOK OF DIFFERENTIAL EQUATIONS, stationary partial differential equations, volume 5 (M. Chipot ed.) , Elservier. pp. 489581.
 Geometrization Program of Semilinear Elliptic Equations 2010 ICCM Proceedings AMS/IP Studies in Advanced Mathematics
 An introduction to the finite and infinite dimensional reduction methods Geometric analysis around scalar curvatures, 35118 Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 31, World Sci. Publ., Hackensack, NJ, 2016.
.
Book
 (with M. Winter) Mathematical Aspects of Pattern Formation in Biological Systems
Applied Mathematical Sciences Series, Vol. 189,
Springer 2014 , ISBN: 978447155256.
Go back to my home page