Multiple solutions of some semilinear elliptic equations via the generalized Conley index
type: Item
instance of: scholarly article
title: Multiple solutions of some semilinear elliptic equations via the generalized Conley index
zbMATH Open document ID: 0834.35049
author: Yihong Du
author: E. N. Dancer
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-07-19T00:00:00Z
review text: The authors use the generalized Conley index to study the existence of several solutions of the problem \(-\Delta u= f(u)\), \(u|_{\partial D} =0\), where \(D\) is a bounded domain in \(\mathbb{R}^n\), and \(f\) is Lipschitz continuous with \(f(0) =0\). Two types of nonlinearities are considered. The first one has a jumping nonlinearity at zero and is sublinear at infinity. The second type is a conjugate case to the first one. In both cases three nontrivial solutions are obtained, one positive, one negative and one changing sign. Previously the existence of a changing sign solution was not known.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 765102
zbMATH Keywords: multiple solutions
zbMATH Keywords: changing sign solution
zbMATH Keywords: generalized Conley index
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1054
OpenAlex ID: W2054435180
DOI: 10.1006/JMAA.1995.1054
description: scientific article; zbMATH DE number 765102