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math.AP2024
Concentration phenomena of positive solutions to weakly coupled Schrödinger systems with large exponents in dimension two
Zhijie Chen, Hanqing Zhao
We study the weakly coupled nonlinear Schrödinger system \begin{equation*} \begin{cases} -Δu_1 = μ_1 u_1^{p} +βu_1^{\frac{p-1}{2}} u_2^{\frac{p+1}{2}}\text{ in } Ω,\\ -Δu_2 = μ_2 u…
math.AP2023★ 1 cited
Energy quantization of the two dimensional Lane-Emden equation with vanishing potentials
Zhijie Chen, Houwang Li
We study the concentration phenomenon of the Lane-Emden equation with vanishing potentials \[\begin{cases} -Δu_n=W_n(x)u_n^{p_n},\quad u_n>0,\quad\text{in}~Ω, u_n=0,\quad\text{on}~…
math.AP2014
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…