Preprints available online


Submitted Papers and Preprints:

  1. (with WW Ao and J. Yang) Vortex helices for inhomogeneous Gross-Pitaevskii equation in three dimensional spaces
  2. (with Andreas Buttenschoen, Theodore Kolokolnikov, and Michael Ward ) Cops-on-the-Dots: The Linear Stability of Crime Hotspots for a 1-D Reaction-Diffusion Model of Urban Crime
  3. (with H. Chan and Y.Liu) A gluing construction for fractional elliptic equations. Part I: a model problem on the catenoid
  4. (with Y. Cheng) fast and slow decaying solutions for $H^1$-supercritical quasilinear Schrodinger equations
  5. (with Juan Davila, Manuel del Pino and Monica Musso) Gluing methods for vortex dynamics in Euler equation
  6. (with Manuel del Pino and Juan Davila) Singularity formation for the two-dimensional harmonic map flow into $S^2$ Singularity formation for the two-dimensional harmonic map flow into $S^2$ (full version)
  7. (with Manuel del Pino and Monica Musso) Geometry driven Type II higher dimensional blow-up for the critical heat equation
  8. (with Manuel del Pino and Monica Musso) Existence and stability of infinite time bubble towers in the energy critical heat equation
  9. (with Y. Ding and Z. Liu) Multiplicity and concentration of semi-classical solutions to nonlinear Dirac equations
  10. (with T. D'Aprile) Bubbling solutions for the Liouville equation with a singular source: non-simple blow-up
  11. (with D. Gomez and L. Mei) Hopf bifurcations from spike solutions for the weak coupling Gierer-Meinhardt system
  12. (with C. Gui and K. Wang) Axially symmetric solutions of Allen-Cahn equation with finite Morse index
  13. (with ZM Guo) Entire solutions and global bifurcations for a biharmonic equation with singular nonlinearity
  14. (with YX Guo) Infinitely many positive solutions for nonlinear Schr\"{o}dinger system with nonsymmetric first order
  15. (with A. Hyder) Non-radial solutions to a bi-harmonic equation with negative exponent
  16. (with A. Hyder and Chang-Shou Lin) On $SU(3)$ Toda system with multiple singular sources
  17. (with A. Hyder and Wen yang) On the general Toda system with multiple singular sources
  18. (with Slim Ibrahim, Hiroaki Kikuchi and Kenji Nakanishi) Non-uniqueness for an energy-critical heat equation on $\R^2$
  19. (with S.Kim and M. Musso) A compactness theorem of the fractional Yamabe problem, Part I: the non-umbilic conformal infinity
  20. (with S.Kim and M. Musso) Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary
  21. (with T. Kolokolnikov) Hexagonal spike clusters for some PDE's in 2D
  22. (with Yong Liu) Nondegeneracy, Morse index and orbital stability of the lump solution to the KP-I equation
  23. (with Yong Liu) A complete classification of finite Morse index solutions to elliptic sine-Gordon equation in the plane
  24. (with Yong Liu and Kelei Wang) On smooth solutions to one phase free boundary problem in $R^n$
  25. (with S Luo and W. Zou) On the triharmonic Lane-Emden equation
  26. (with S Luo and W. Zou) Classification of stable solutions to the fractional ($2
  27. (with S Luo and W. Zou) On finite Morse index solutions to the quaharmonic Lane-Emden equations
  28. (with S Luo and X. Ren) Non-hexagonal lattices from a two species interacting system
  29. (with CS Lin and Z. Nie) Classification of solutions to general Toda systems with singular sources
  30. (with H. Matano) On anisotropic curvature flows (paper written in 1997)
  31. (with Y. Sire and Y. Zheng) Infinite time blow-up for half-harmonic map flow from $\mathbb{R}$ into $\mathbb{S}^1$
  32. (with Y. Sire and Y. Zheng) Singularity formation in the harmonic map flow with free boundary
  33. (with Kelei Wang) Second order estimates on transition layers
  34. (with M. Winter) Stability of new spike solutions in a supply chain model
  35. (with Y. Wu) Ground states of Nonlinear Schr\"{o}dinger System with Mixed Couplings
  36. (with Lei Zhang) Estimates for Liouville equation with quantized singularities
  37. (with Liqun Zhang) On the effect of domain shape on the existence of large solutions of some spuerlinear elliptic problems,


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