Liouville-type theorems for generalized Hénon-Lane-Emden Schrödinger systems in $\mathbb R^2$ and $\mathbb R^3$

Abstract

In the paper we study the Liouville-type theorems for generalized Hénon-Lane-Emden elliptic system in $\mathbb{R}^N$. By the methods of spherical averages, Rellich-Pohozaev type identities, Sobolev inequalities on $S^{N-1}$, feedback and measure arguments, and scale invariance of the solutions, we show that if the pair of exponents is subcritical, then this system has no positive solutions for $N=2$ and no bounded positive solutions for $N=3$.