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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
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…
math.AP2023
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…