A note on additional properties of sign changing solutions to superlinear elliptic equations
type: Item
instance of: scholarly article
title: A note on additional properties of sign changing solutions to superlinear elliptic equations
zbMATH Open document ID: 1094.35041
DOI: 10.12775/TMNA.2003.025
author: Thomas J. Bartsch
author: Tobias Weth
published in: Topological Methods in Nonlinear Analysis
publication date: 2004-09-06T00:00:00Z
review text: The authors deal with sign-changing solutions of the semilinear Dirichlet problem \[ -\Delta u=f(x,u) \quad\text{for }x\in\Omega, \qquad u=0 \quad\text{for }x\in\partial\Omega, \] where \(\Omega\) is a bounded smooth domain in \(\mathbb R^N\), \(N\geq 2\). Under some natural assumptions on \(f\), the authors using suitable min-max descriptions obtain upper bounds for the number of nodal domains of sign changing solutions for (1). Moreover, they also obtain information on the Morse index of solutions and the location of sub- and supersolutions.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2096714
zbMATH Keywords: sign-changing solutions
zbMATH Keywords: superlinear elliptic equation
zbMATH Keywords: Morse index
zbMATH Keywords: nodal domains
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: tmna.2003.025
OpenAlex ID: W2548191185
description: scientific article; zbMATH DE number 2096714