Liouville-type theorems for generalized Hénon-Lane-Emden Schrödinger systems in $R^2$ and $R^3$ - Cheng, Xiyou; Li, Kui; Zhang, Zhitao (Topological Methods in Nonlinear Analysis, 2022)
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 $N=3$.