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2022 Liouville-type theorems for generalized Hénon-Lane-Emden Schrödinger systems in $\mathbb R^2$ and $\mathbb R^3$
Xiyou Cheng, Kui Li, Zhitao Zhang
Topol. Methods Nonlinear Anal. 59(1): 331-357 (2022). DOI: 10.12775/TMNA.2021.028

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 $N=3$.

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Xiyou Cheng. Kui Li. Zhitao Zhang. "Liouville-type theorems for generalized Hénon-Lane-Emden Schrödinger systems in $\mathbb R^2$ and $\mathbb R^3$." Topol. Methods Nonlinear Anal. 59 (1) 331 - 357, 2022. https://doi.org/10.12775/TMNA.2021.028

Information

Published: 2022
First available in Project Euclid: 3 June 2021

Digital Object Identifier: 10.12775/TMNA.2021.028

Keywords: Liouville-type theorem , Nonlinear elliptic weighted system , ‎positive‎ ‎solutions , Schrödinger system

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.59 • No. 1 • 2022
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