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math.AP2025
On a new region for the Lane-Emden conjecture in higher dimensions
Kui Li, Mingxiang Li, Juncheng Wei
We study the Lane-Emden conjecture, which asserts the non-existence of non-trivial, non-negative solutions to the Lane-Emden system \[ -Δu = v^p, \quad -Δv = u^q, \quad x \in \math…
math.AP2025
Symmetry and classification of positive solutions of some weighted elliptic equations
Kui Li, Mengyao Liu, Jianfeng Wu
We study the weighted elliptic equation \begin{equation} -div(|x|^{-2a}\nabla u)=|x|^{-bp}|u|^{p-2}u~~~\mbox{in}~\mathbb{R}^N ~~~~~~~~~~~~~~~~~~~~(0.1)\end{equation} with …