On the solution set of some classes of nonconvex nonclosed differential inclusions
type: Item
instance of: scholarly article
title: On the solution set of some classes of nonconvex nonclosed differential inclusions
zbMATH Open document ID: 1165.34039
DOI: 10.4171/PM/1822
author: Aurelian Cernea
published in: Portugaliae Mathematica. Nova Série
publication date: 2008-12-11T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: The author studies the following semilinear differential inclusion \[ x'\in Ax+F(t,x,H(t,x)), \quad x(0)=x_0, \] where \(X\) is a real separable Banach space, \(F:[0,T]\times X^2 \to 2^X\) and \(H:[0,T]\times X \to 2^X\) are two multifunctions with nonempty values, \(A\) is the infinitesimal generator of strongly continuous semigroups \(\{G(t): t\geq 0\}\) on \(X\). In the main result, the arcwise connectedness of the solution set of the above problem is proved in the case that \(F\) and \(H\) are Lipschitzian with respect to the second variable and \(F\) is contractive in the third variable. A similar result is stated also for a class of second order differential inclusions.
reviewed by: Francesca Papalini
Mathematics Subject Classification ID: 34G25
zbMATH DE Number: 5381762
zbMATH Keywords: set-valued contraction
zbMATH Keywords: fixed point
zbMATH Keywords: semilinear differential inclusions
zbMATH Keywords: cosine family of opeartors
MaRDI profile type: Publication
cites work: On second-order differential inclusions in Banach spaces
OpenAlex ID: W2039309442
description: scientific article; zbMATH DE number 5381762