Existence and multiplicity of solutions for second order periodic systems with the \(p\)-Laplacian and a nonsmooth potential
type: Item
instance of: scholarly article
title: Existence and multiplicity of solutions for second order periodic systems with the \(p\)-Laplacian and a nonsmooth potential
zbMATH Open document ID: 1187.34020
author: Nikolaos S. Papageorgiou
author: Leszek Gasiński
published in: Monatshefte für Mathematik
publication date: 2009-10-14T00:00:00Z
review text: The authors deals with the fractional boundary value problem for a differential inclusion \[ \begin{cases} (\|x'(t)\|^{p-2}x'(t))' \in \partial j(t,x(t))\;&\text{ a.e. } \, t\in (0,T) ,\\ x(0)=x(T),\quad x'(0)=x'(T), \end{cases}\tag{1} \] where \(1<p<+\infty,\) \(j: [0,T]\times\mathbb R^N\to\mathbb R^N\) and \(\partial j(t,\xi)\) is a subdifferential in the sense of \textit{F. H. Clarke} [Optimization and nonsmooth analysis. New York: John Wiley \& Sons (1983; Zbl 0582.49001)]. Questions of interest involve the existence and multiplicity of solutions for (1). Methods used include applications of nonsmoth second deformation lemma and nonsmooth local linking theorem.
reviewed by: Abdelghani Ouahab
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5614961
zbMATH Keywords: multiplicity of solutions
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: periodic system
zbMATH Keywords: reduction method
zbMATH Keywords: second deformation lemma
zbMATH Keywords: locally Lipschitz potential
zbMATH Keywords: local linking
MaRDI profile type: Publication
Wikidata QID: Q112251819
full work available at URL: s00605-008-0041-7
OpenAlex ID: W2461910814
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DOI: 10.1007/S00605-008-0041-7
description: scientific article; zbMATH DE number 5614961