Preprints available online
Submitted Papers and Preprints:
 (with W. Ao, H. Chan, Mar Gonzalez)
Bound state solutions for the supercritical fractional Schrodinger equation
 (with W. Ao H. Chan, A. Delatorre, M. Fontelos Mar Gonzalez)
On higher dimensional singularities for the fractional Yamabe problem: a nonlocal MazzeoPacard program
 (with WW Ao and J. Yang)
Vortex helices for inhomogeneous GrossPitaevskii equation in three dimensional spaces
 (with Andreas Buttenschoen, Theodore Kolokolnikov, and Michael Ward )
CopsontheDots: The Linear Stability of Crime Hotspots for a 1D ReactionDiffusion Model of Urban Crime
 (with H. Chan and Y.Liu)
A gluing construction for fractional elliptic equations. Part I: a model problem on the catenoid
 (with G. Chen and Y.Liu)
Nondegeneracy of harmonic maps from $\mathbb R^2$ to $\mathbb S^2$
 (with G. Chen and Y.Zhou)
Finite time blow ups for fractional critical heat equations
 (with Juan Davila, Manuel del Pino and Monica Musso)
Gluing methods for vortex dynamics in Euler equation
 (with Juan Davila, Manuel del Pino and Catalina Pesce)
Blowup for the 3dimensional axially symmetric harmonic map flow into $S^2$
 (with Manuel del Pino and Juan Davila)
Singularity formation for the twodimensional harmonic map flow into $S^2$
 (with Manuel del Pino and Monica Musso)
Type II blowup in the 5dimensional energy critical heat equation
 (with Manuel del Pino and Monica Musso)
Infinite time blowup for the three dimensional energy critical heat equation
 (with Manuel del Pino and Monica Musso)
Geometry driven Type II higher dimensional blowup for the critical heat equation
 (with Manuel del Pino, Monica Musso and Y. Zheng)
Signchanging blowingup solutions for the critical nonlinear heat equation
 (with Y. Ding and Z. Liu) Multiplicity and concentration of
semiclassical solutions
to nonlinear Dirac equations
 (with D. Gomez and L. Mei) Hopf bifurcations from spike solutions for the weak coupling GiererMeinhardt system
 (with D. Gomez and L. Mei) Stable and unstable perioidc spiky solutions for the GrayScott system and the Schnakenberg system
 (with D. Gomez and M.J. Ward) The linear stability of symmetric spike patterns for a bulkmembrane coupled GiererMeinhardt model
 (with ZM Guo)
Entire solutions and global bifurcations for a biharmonic equation with singular nonlinearity
 (with YX Guo)
Infinitely many positive solutions for nonlinear Schr\"{o}dinger system with nonsymmetric first order
 (with A. Hyder)
Nonradial solutions to a biharmonic equation with negative exponent
 (with A. Hyder)
Higher order conformally invariant equations in $R^3$ with prescribed volume
 (with S.Kim and M. Musso)
A compactness theorem of the fractional Yamabe problem, Part I: the nonumbilic conformal infinity
 (with T. Kolokolnikov)
Hexagonal spike clusters for some PDE's in 2D
 (with Yong Liu)
Nondegeneracy, Morse index and orbital stability of the lump solution to the KPI equation
 (with Yong Liu)
Multivortex traveling waves for the GrossPitaevskii equation and the
AdlerMoser polynomials
 (with Yong Liu)
A complete classification of finite Morse index solutions to elliptic
sineGordon equation in the plane
 (with Yong Liu and Kelei Wang)
On smooth solutions to one phase free boundary problem in $R^n$
 (with S Luo and W. Zou)
On the triharmonic LaneEmden equation
 (with S Luo and W. Zou)
Classification of stable solutions to the fractional ($2
 (with S Luo and W. Zou)
On finite Morse index solutions to the quaharmonic LaneEmden equations

(with S Luo and X. Ren)
Nonhexagonal lattices from a two species interacting system
 (with CS Lin and Z. Nie)
Classification of solutions to general Toda systems with singular sources

(with H. Matano)
On anisotropic curvature flows (paper written in 1997)

(with M. Musso, M. Medina)
Desingularization of Clifford Torus and Nonradial Solutions to Yamabe
Problem with Maximal Rank

(with Y. Sire and Y. Zheng)
Infinite time blowup for halfharmonic map flow from $\mathbb{R}$ into $\mathbb{S}^1$

(with Kelei Wang)
Second order estimates on transition layers
 (with M. Winter)
Stability of new spike solutions in a supply chain model

(with Liqun Zhang)
On the effect of domain shape on the existence of large solutions of some spuerlinear elliptic problems,
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