173 citations · 228 across the 28 of their papers we have counts for
16 papers · 1 filter
Geometric analysis on rhombus torus: Green function with two singularities
Zhijie Chen, Erjuan Fu, Chang-Shou Lin +1
Let be the Green function on the flat torus with the singularity at . Lin and Wang (Ann. Math. 2010) proved that has at m…
Sovability of curvature equations with multiple singular sources on torus via Painleve VI equations
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
We study the curvature equation with multiple singular sources on a torus \[Δu+e^{u}=8π\sum_{k=0}^{3}n_{k}δ_{\frac{ω_{k}}{2}}% +4π\left( δ_{p}+δ_{-p}\right) \quad \text{ on }\;E_τ:…
Generic non-degeneracy of critical points of multiple Green functions on torus and applications to curvature equations
Zhijie Chen, Erjuan Fu, Chang-Shou Lin
Let with be a flat torus and be the Green function on with the singularity at . Consider the mul…
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane-Emden equation in dimension two
Zhijie Chen, Zetao Cheng, Hanqing Zhao
We study the Lane-Emden problem \[\begin{cases} -Δu_p =|u_p|^{p-1}u_p&\text{in}\quad Ω, u_p=0 &\text{on}\quad\partialΩ, \end{cases}\] where is a smooth bounde…
Asymptotic behavior of least energy nodal solutions for biharmonic Lane-Emden problems in dimension four
Zhijie Chen, Zetao Cheng, Hanqing Zhao
In this paper, we study the asymptotic behavior of least energy nodal solutions to the following fourth-order elliptic problem \[ \begin{cases} Δ^2 u =|u|^{p-1}u \quad &\h…
Sharp estimates, uniqueness and nondegeneracy of positive solutions of the Lane-Emden system in planar domains
Zhijie Chen, Houwang Li, Wenming Zou
We study the Lane-Emden system where $Ω\subset…
On number and evenness of solutions of the Toda system on flat tori with non-critical parameters
Zhijie Chen, Chang-Shou Lin
We study the Toda system with singular sources \[ \begin{cases} Δu+2e^{u}-e^v=4π\sum_{k=0}^m n_{1,k}δ_{p_k}\quad\text{ on }\; E_τ,\\ Δv+2e^{v}-e^u=4π\sum_{k=0}^m n_{2,k}δ_{…
Sharp nonexistence results for curvature equations with four singular sources on rectangular tori
Zhijie Chen, Chang-Shou Lin
In this paper, we prove that there are no solutions for the curvature equation \[ Δu+e^{u}=8πnδ_{0}\text{ on }E_τ, \quad n\in\mathbb{N}, \] where is a flat rectangular torus…
Non-existence of solutions for a mean field equation on flat tori at critical parameter
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
It is known from \cite{LW} that the solvability of the mean field equation with on a flat torus essentially depends on the geome…
A new type of non-topological bubbling solutions to a competitive Chern-Simons model
Zhijie Chen, Chang-Shou Lin
We study a non-Abelian Chern-Simons system in , including the simple Lie algebras and . In a previous work, we proved the existence of radial non-topologic…
Removable singularity of positive solutions for a critical elliptic system with isolated singularity
Zhijie Chen, Chang-Shou Lin
We study qualitative properties of positive singular solutions to a two-coupled elliptic system with critical exponents. This system is related to coupled nonlinear Schrodinger equ…
Multiple sign-changing and semi-nodal solutions for coupled Schrodinger equations
Zhijie Chen, Chang-Shou Lin, Wenming Zou
We study the following coupled Schrödinger equations which have appeared as several models from mathematical physics: \begin{displaymath} \begin{cases}-Δu_1 +\la_1 u_1 = μ_1 u_1^3+…
Standing waves for coupled nonlinear Schrodinger equations with decaying potentials
Zhijie Chen, Wenming Zou
We study the following singularly perturbed problem for a coupled nonlinear Schrödinger system: {displaymath} {cases}-\e^2Δu +a(x) u = μ_1 u^3+βuv^2, \quad x\in \R^3, -\e^2Δv +b(x)…
Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system
Zhijie Chen, Chang-Shou Lin, Wenming Zou
We study the following coupled Schrödinger equations which have appeared as several models from mathematical physics: {displaymath} {cases}-Δu_1 +\la_1 u_1 = μ_1 u_1^3+βu_1 u_2^2,…
Standing Waves for nonlinear Schrodinger Equations involving critical growth
Jianjun Zhang, Zhijie Chen, Wenming Zou
We consider the following singularly perturbed nonlinear elliptic problem: $$-\e^2Δu+V(x)u=f(u),\ u\in H^1(\mathbb{R^N}),$$ where and the nonlinearity is of critical g…
Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case
Zhijie Chen, Wenming Zou
We study the following nonlinear Schrödinger system which is related to Bose-Einstein condensate: {displaymath} {cases}-Δu +\la_1 u = μ_1 u^{2^\ast-1}+βu^{\frac{2^\ast}{2}-1}v^{\fr…