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 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.