Existence of positive and of multiple solutions for nonlinear periodic problems
type: Item
instance of: scholarly article
title: Existence of positive and of multiple solutions for nonlinear periodic problems
zbMATH Open document ID: 1120.34012
author: Leszek Gasiński
author: Nikolaos S. Papageorgiou
author: Zdzisław Denkowski
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-04-19T00:00:00Z
review text: The paper deals with the study of a scalar periodic problem of the following form: \[ -(| x'(t)| ^{p-2}x'(t))'\in \partial j(t,x(t))\quad\text{for a.a. }t\in T=[0,b], \] \[ x(0)=x(b),\quad x'(0)=x'(b), \] where \(\partial j(t,\cdot)\) denotes the generalized subdifferential, \(1<p<+\infty,\, j:T\times \mathbb R\to \mathbb R\) is a measurable function such that for almost all \(t\in T,\) \(j(t,\cdot)\) is locally Lipschitz. Applying the nonsmooth critical point theory, the authors obtain some results on the existence of a strictly positive and of multiple solutions.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5144894
zbMATH Keywords: locally Lipschitz functions
zbMATH Keywords: Clarke subdifferential
zbMATH Keywords: nonsmooth Cerami condition
zbMATH Keywords: generalized nonsmooth Palais-Smale condition
zbMATH Keywords: local minimum
zbMATH Keywords: nonsmooth mountain pass theorem
MaRDI profile type: Publication
full work available at URL: j.na.2006.03.020
OpenAlex ID: W2003826256
Wikidata QID: Q112251830
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DOI: 10.1016/J.NA.2006.03.020
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description: scientific article; zbMATH DE number 5144894