Liouville-type theorems for generalized Hénon-Lane-Emden Schrödinger systems in $R^2$ and $R^3$
DOI:
https://doi.org/10.12775/TMNA.2021.028Keywords
Nonlinear elliptic weighted system, Schrödinger system, positive solutions, Liouville-type theoremAbstract
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 $N=3$.References
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