Some Liouville theorems for Hénon type elliptic equations
type: Item
instance of: scholarly article
title: Some Liouville theorems for Hénon type elliptic equations
zbMATH Open document ID: 1246.35092
author: Chao Wang
author: Dong Ye
published in: Journal of Functional Analysis
publication date: 2012-03-05T00:00:00Z
review text: In this paper the authors investigate the nonlinear elliptic equations \(-\Delta u=|x|^{\alpha_{e}u}\) and \(-\Delta u=|x|^{\alpha}|u|^{p-1}u\) with \(\alpha>-2, \;p>1\) and \(N\geqslant2\). The main objective of this paper is to classify such weak solutions of both problems under consideration in \(\mathbb R^{N}\) that are stable outside a compact set or which have finite Morse index in the low dimensional Euclidean spaces or half spaces.
reviewed by: Marek Galewski
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35B53
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6012143
zbMATH Keywords: Liouville theorem
zbMATH Keywords: Hénon equation
zbMATH Keywords: stability
zbMATH Keywords: finite Morse index solution
MaRDI profile type: Publication
full work available at URL: j.jfa.2011.11.017
OpenAlex ID: W2060779723
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DOI: 10.1016/J.JFA.2011.11.017
description: scientific article; zbMATH DE number 6012143