Liouville type theorems for stable solutions of the weighted elliptic system with the advection term: \(p \geq \vartheta >1\)
type: Item
instance of: scholarly article
title: Liouville type theorems for stable solutions of the weighted elliptic system with the advection term: \(p \geq \vartheta >1\)
zbMATH Open document ID: 1391.35090
author: Lianggen Hu
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2018-03-14T00:00:00Z
review text: This paper concerns the nonexistence of classical positive stable solutions for the weighted elliptic system \[ -\omega(x)\Delta u-\nabla w(x)\cdot \nabla u=\omega_1 v^{\vartheta}, \] \[ -\omega(x)\Delta v-\nabla w(x)\cdot \nabla v=\omega_2 v^p, \] posed in \(\mathbb{R}^N\), \(N\geq 3\), \(p\geq \vartheta >1\) and \(\omega, \omega_1,\omega_2\) satisfy some appropriate conditions. The two main results of the paper establish that under some extra conditions on exponents and weights, the above system has no classical positive stable solutions.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35B53
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J47
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 6850164
zbMATH Keywords: nonexistence of classical positive stable solutions
MaRDI profile type: Publication
full work available at URL: s00030-018-0498-6
OpenAlex ID: W2792440356
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DOI: 10.1007/S00030-018-0498-6
description: scientific article; zbMATH DE number 6850164