A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
type: Item
instance of: scholarly article
title: A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
zbMATH Open document ID: 1081.49002
author: Ryuji Kajikiya
published in: Journal of Functional Analysis
publication date: 2005-09-22T00:00:00Z
review text: In this paper it is proved a critical point theorem of mountain-pass type which yields a sequence of critical points converging to zero. The proof combines a pseudo-gradient property with a deformation lemma. The abstract result is applied for proving a multiplicity result for the semilinear elliptic equation \(-\Delta u=f(x,u)\) in \(\Omega\) under the Dirichlet boundary condition \(u=0\) on \(\partial\Omega\), where \(\Omega\) is a bounded domain in \(\mathbb R^n\) with a smooth boundary and \(f(x,u)\) behaves like \(a(x)| u| ^p\)sgn\(\, u\) with \(0<p<1\).
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2207242
zbMATH Keywords: symmetric mountain pass lemma
zbMATH Keywords: critical point theorem
zbMATH Keywords: variational method
zbMATH Keywords: semilinear elliptic equation
MaRDI profile type: Publication
full work available at URL: j.jfa.2005.04.005
OpenAlex ID: W2077629107
Wikidata QID: Q124879786
cites work: Dual variational methods in critical point theory and applications
cites work: Q5636090
cites work: Multiple existence of non-radial solutions with group invariance for sublinear elliptic equations
cites work: Q3749777
cites work: Q4714152
DOI: 10.1016/J.JFA.2005.04.005
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description: scientific article