Liouville theorems for stable at infinity solutions of Lane-Emden system

Abstract

We consider the Lane-Emden system $-\Delta u=v^p$, $-\Delta v=u^{\theta }$ in ${\mathbb{R}}^N$, and we prove the nonexistence of smooth positive solutions which are stable outside a compact set, for any $p,\theta >0$ under the Sobolev hyperbola.