A critical point theorem with a relaxed boundary condition and critical groups
type: Item
instance of: scholarly article
title: A critical point theorem with a relaxed boundary condition and critical groups
zbMATH Open document ID: 0953.58008
DOI: 10.1016/S0362-546X(98)00229-6
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-01-22T00:00:00Z
review text: A critical point theorem with an information on the Morse critical groups has been proved by the author in [J. Differ. Equations 140, No. 1, 142-160 (1997; Zbl 0889.58025)]. In the present paper the author extends this result to the case of the so-called relaxed boundary conditions in the spirit of \textit{N. Ghoussoub} [Proc. Am. Math. Soc. 117, No. 2, 439-447 (1993; Zbl 0791.49028)]. As an application a new multiplicity result for a superlinear Sturm-Liouville equation under Neumann boundary condition is given. Information on the critical groups from the abstract theorem is used to distinguish between constant and nonconstant solutions.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1419540
zbMATH Keywords: critical point theory
zbMATH Keywords: Morse theory
zbMATH Keywords: homological linking
zbMATH Keywords: critical groups
author: Kanishka Perera
reviewed by: Vitaly Moroz
MaRDI profile type: Publication
Wikidata QID: Q126437588
full work available at URL: s0362-546x(98)00229-6
OpenAlex ID: W1998809269
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description: scientific article; zbMATH DE number 1419540