Ljusternik-Schnirelmann theory on \(C^ 1\)-manifolds
type: Item
instance of: scholarly article
title: Ljusternik-Schnirelmann theory on \(C^ 1\)-manifolds
zbMATH Open document ID: 0661.58009
DOI: 10.1016/S0294-1449(16)30348-1
author: Andrzej Szulkin
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78147
review text: The author extends to \(C^ 1\) manifolds the Lyusternik-Schnirelman theory. More precisely, let M be a complete Finsler manifold of class \(C^ 1\). It is shown that, if M contains a compact subset of category k in M, then each function \(f\in C^ 1(M,{\mathbb{R}})\) which is bounded from below and satisfies the Palais-Smale condition must necessarily have k critical points. The proof depends on an interesting application of Ekeland's variational principle. An application is given to an eigenvalue problem for a quasilinear differential equation involving the p- Laplacian.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 4080439
zbMATH Keywords: Lyusternik-Schnirelman theory
zbMATH Keywords: Palais-Smale condition
zbMATH Keywords: critical points
zbMATH Keywords: Ekeland's variational principle
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: quasilinear differential equation
zbMATH Keywords: p-Laplacian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4080439