Critical points when there is no saddle point geometry
type: Item
instance of: scholarly article
title: Critical points when there is no saddle point geometry
zbMATH Open document ID: 0864.58007
DOI: 10.12775/TMNA.1995.047
published in: Topological Methods in Nonlinear Analysis
publication date: 1997-07-06T00:00:00Z
review text: Using the topological method of linking subsets [the author and \textit{K. Tintarev}, Bull. Soc. Math. Belg., Sér. B 44, 249-261 (1992; Zbl 0785.58017)]the author proves two abstract theorems that imply certain extensions of the saddle point theorem of \textit{P. H. Rabinowitz} [Reg. Conf. Ser. Math. 65 (1986; Zbl 0609.58002)]. The results are then used to obtain the existence of nontrivial solutions of semilinear elliptic boundary value problems of the form \(Au=f(x,u)\).
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35J50
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 929672
zbMATH Keywords: critical point
zbMATH Keywords: linking subsets
zbMATH Keywords: saddle point
zbMATH Keywords: elliptic boundary value problems
author: Martin Schechter
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
full work available at URL: tmna.1995.047
OpenAlex ID: W2587493217
description: scientific article; zbMATH DE number 929672