Qualitative properties for semilinear elliptic systems with non-Lipschitz nonlinearity
type: Item
instance of: scholarly article
title: Qualitative properties for semilinear elliptic systems with non-Lipschitz nonlinearity
zbMATH Open document ID: 1012.35024
DOI: 10.1016/S0362-546X(01)00761-1
author: Jérôme Busca
author: Alexander Quaas
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: This paper is devoted to study symmetry properties for elliptic systems, the model problem of which has the form: \[ \begin{cases} \Delta u-u^p+ v^q=0 \quad & \text{in }\mathbb{R}^N\\ \Delta v-v^p+ u^q=0 \quad & \text{in }\mathbb{R}^N, \end{cases} \tag{1} \] where \(0<p< 1<q\), \(u,v\geq 0\), \(u,v\to 0\) as \(|x|\to \infty\). The authors present a symmetry result in the case of non-Lipschitzian nonlinearities. A proof of the main symmetry result for (1) is based on an adaptation of the well-known moving planes method, which crucially relies on some integral form of the maximum principle, developed by the authors in this paper. A more general class of nonlinearities is investigated as well.
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 1788012
zbMATH Keywords: symmetry property
zbMATH Keywords: maximum principle
zbMATH Keywords: moving planes method
zbMATH Keywords: integral form
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1788012