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math.AP2023★ 1 cited
Existence of Boundary Layers for the supercritical Lane-Emden Systems
Qing Guo, Junyuan Liu, Shuangjie Peng
We consider the following supercritical problem for the Lane-Emden system: \begin{equation}\label{eq00} \begin{cases} -Δu_1=|u_2|^{p-1}u_2\ &in\ D,\\ -Δu_2=|u_1|^{q-1}u_1 \ &in\ D,…
math.AP2023★ 3 cited
Sign-changing solutions to the slightly supercritical Lane-Emden system with Neumann boundary conditions
Qing Guo, Shuangjie Peng
We consider the following slightly supercritical problem for the Lane-Emden system with Neumann boundary conditions: \begin{equation*} \begin{cases} -Δu_1=|u_2|^{p_ε-1}u_2,\ &in\ Ω…