Periodic problems for strongly nonlinear second-order differential inclusions
type: Item
instance of: scholarly article
title: Periodic problems for strongly nonlinear second-order differential inclusions
zbMATH Open document ID: 1022.34008
author: Nikolaos Matzakos
author: Nikolaos S. Papageorgiou
author: Sophia Th. Kyritsi
published in: Journal of Differential Equations
publication date: 2002-11-28T00:00:00Z
review text: The authors study the following nonlinear, second-order periodic problem in \(\mathbb{R}^N\) \[ a(x'(t))'\in Ax(t)+F(t,x(t),x'(t))\text{ a.e. on }T,\quad x(0)=x(b),\;x'(0)=x'(b), \] where \(a:\mathbb{R}^N\rightarrow\mathbb{R}^N\) and \(A:\mathbb{R}^N\rightarrow 2^{\mathbb{R}^N}\) are maximal monotone maps and \(F\) is a multifunction. The hypotheses they use on the nonlinear differential operator do not assume any homogeneity nor any growth condition. Moreover, they allow the operator \(A\) to be either defined everywhere on \(\mathbb{R}^N\) or not. The methods used come from multivalued analysis and from the theory of operators of monotone type. The existence of solutions for both the ``convex'' and the ``nonconvex'' problem is proved.
reviewed by: Nikos Yannakakis
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1836797
zbMATH Keywords: differential inclusions
zbMATH Keywords: second-order equation
zbMATH Keywords: periodic problem
zbMATH Keywords: maximal monotone map
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: Leray-Schauder alternative theorem
zbMATH Keywords: fixed-point problem
zbMATH Keywords: set-valued function
zbMATH Keywords: measurable selection
zbMATH Keywords: continuous selection
zbMATH Keywords: Nagumo-Hartman condition
zbMATH Keywords: Yosida approximation
MaRDI profile type: Publication
full work available at URL: jdeq.2001.4110
OpenAlex ID: W2063105637
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DOI: 10.1006/JDEQ.2001.4110
description: scientific article; zbMATH DE number 1836797