Anti-periodic solutions for nonlinear evolution inclusions
type: Item
instance of: scholarly article
title: Anti-periodic solutions for nonlinear evolution inclusions
zbMATH Open document ID: 1401.34072
author: Leszek Gasiński
author: Nikolaos S. Papageorgiou
published in: Journal of Evolution Equations
publication date: 2018-09-05T00:00:00Z
review text: The authors consider the nonlinear anti-periodic evolution inclusion \[ \begin{aligned} & -u'(t)\in A(t,u(t))+F(t,u(t))\text{ a.e. on }I=[0,T],\\ & u(0)=-u(T),\end{aligned}\eqno{(1)} \] where \(\left( X,H,X^{\ast }\right) \) is an evolution triple, \(A:I\times X\rightarrow 2^{X^{\ast }}\) and \(F:I\times X\rightarrow 2^{H}\). \ It is not assumed that \(A(t,\cdot )\) is maximal monotone or that \(F(t,\cdot )\) is a subdifferential. \ Existence is proven for the case in which \(F\) is convex-valued and also in the case in which it is not necessarily convex-valued. \ Also, existence is proven when \(F\) is replaced by its extreme points. \ It is then shown that the extremal trajectories are dense in the set of solutions of the convex problem. \ An example is given to illustrate this last result. \ The proofs make use of the selection theorem from [\textit{A. Bressan} and \textit{G. Colombo}, Stud. Math. 90, No. 1, 69--86 (1988; Zbl 0677.54013)] and a number of other results from the literature, including the monographs by Hu and Papageorgiou.
reviewed by: Daniel C. Biles
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 6932132
zbMATH Keywords: nonlinear evolution inclusion
zbMATH Keywords: anti-periodic
zbMATH Keywords: evolution triple
zbMATH Keywords: extremal trajectories
zbMATH Keywords: relaxation
zbMATH Keywords: convex
zbMATH Keywords: nonconvex
MaRDI profile type: Publication
full work available at URL: s00028-018-0431-9
OpenAlex ID: W2789709806
Wikidata QID: Q112251714
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DOI: 10.1007/S00028-018-0431-9
description: scientific article; zbMATH DE number 6932132