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 \ma…