Positive solutions for nonlinear periodic problems with the scalar \(p\)-Laplacian
type: Item
instance of: scholarly article
title: Positive solutions for nonlinear periodic problems with the scalar \(p\)-Laplacian
zbMATH Open document ID: 1172.34005
author: Leszek Gasiński
author: Zdzisław Denkowski
author: Nikolaos S. Papageorgiou
published in: Set-Valued Analysis
publication date: 2009-03-16T00:00:00Z
review text: The authors study the existence of positive solutions for the following nonlinear periodic problem with nonsmooth potential (hemivariational inequality): \[ -(|x'(t)|^{p-2}x'(t))'\in \partial j(t,x(t)), \text{ for a.a. } t \in T=[0,b], \] \[ x(0)=x(b), \qquad x'(0)=x'(b), \] where \(1<p<+\infty\). \(\partial j(t,x)\) denotes the generalized (Clarke) subdifferential with respect to the variable \(x\) of the function \(j:T\times \mathbb R\to\mathbb R\) which is locally Lipschitz and not necessarily \(C^1\) in the \(x\)-variable. They assume a nonuniform nonresonance condition at \(+\infty\) and a uniform nonresonance condition at \(0^+\) and, using degree theoretic argument based on a fixed point index for certain nonconvex valued multifunctions, they prove the existence of a strictly positive solution.
reviewed by: Francesca Papalini
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5529263
zbMATH Keywords: nonsmooth potential
zbMATH Keywords: scalar p-Laplacian
zbMATH Keywords: generalized subdifferential
zbMATH Keywords: weighted eigenvalue problem
zbMATH Keywords: nonuniform nonresonance
zbMATH Keywords: fixed point index
MaRDI profile type: Publication
full work available at URL: s11228-007-0059-3
OpenAlex ID: W2077991269
Wikidata QID: Q112251825
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DOI: 10.1007/S11228-007-0059-3
description: scientific article; zbMATH DE number 5529263