New result on Lane-Emden conjecture with exponents in a disk

Haoyang Lu, Zhitao Zhang

We obtain new results on Lane-Emden conjecture to prove a Liouville theorem for the Lane-Emden system $$\begin{cases} -Δu=v^p,& x\in \mathbb{R}^N,\\ -Δv=u^q,& x\in \mathbb{R}^N,\en…