On the Morse indices of sign changing solutions of nonlinear elliptic problems
type: Item
instance of: scholarly article
title: On the Morse indices of sign changing solutions of nonlinear elliptic problems
zbMATH Open document ID: 0946.35023
author: Zhi-Qiang Wang
author: Thomas J. Bartsch
author: Kung Ching Chang
published in: Mathematische Zeitschrift
publication date: 2000-10-10T00:00:00Z
review text: Let \(f\colon {\mathbb{R}}\to {\mathbb{R}}\) be of class \({\mathcal C}^1\) with \(f(0)=0\) and consider the problem (D) \(-\Delta u=f(u)\) in a Lipschitz bounded domain of \({\mathbb{R}}^N\) with Dirichlet boundary data. The Morse index and the sign of the solutions of (D) are investigated by some new abstract critical point theorems for functionals on partially ordered Hilbert spaces. This additional information is used to establish the existence of multiple solutions of (D). Under quite similar conditions on the partial order used and on the functional appearing in the abstract results established there, a ``Mountain Pass Theorem in order intervals'' was recently established by Shujie Li and the third author that was applied to study the existence of multiple solutions and sign-changing solutions of some elliptic problems.
reviewed by: Youssef Jabri
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 1463420
zbMATH Keywords: Morse index
zbMATH Keywords: sign-changing solutions
zbMATH Keywords: partial order
zbMATH Keywords: multiplicity
MaRDI profile type: Publication
full work available at URL: s002090050492
OpenAlex ID: W2092781458
DOI: 10.1007/S002090050492
description: scientific article; zbMATH DE number 1463420