On the number of positive symmetric solutions of a nonautonomous semilinear elliptic problem
type: Item
instance of: scholarly article
title: On the number of positive symmetric solutions of a nonautonomous semilinear elliptic problem
zbMATH Open document ID: 0961.35055
DOI: 10.1016/S0362-546X(98)00354-X
author: Mónica Clapp
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-05-15T00:00:00Z
review text: The author considers the problem \[ -\Delta u+a(x)u=K(x)|u|^{p-2}u \quad \text{in }\Omega ,\qquad u>0\quad \text{in } \Omega ,\qquad u=0\quad \text{on } \partial \Omega , \] where \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^n\), \(a\), \(K\) are continuous, \(a\geq 0\), \(K>0,\) and \(2<p\leq 2n/(n-2)\). Moreover, \(\Omega\), \(a\), \(K\) are supposed to be invariant under the action of a closed subgroup \(G\) of the orthogonal group of \(\mathbb{R}^n\). The lower estimate of the number of \(G\)-invariant solutions is given (for \(p\) close to \(2n/(n-2)\)) in terms of the Lusternik-Shnirelmann category of the set of \(G\)-maximal values of \(K\).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1512513
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: nonautonomous elliptic equations
zbMATH Keywords: multiple positive symmetric solutions
reviewed by: E. A. Kalita
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1512513