Continuous selection of the solution map for one-sided Lipschitz differential inclusions
type: Item
instance of: scholarly article
title: Continuous selection of the solution map for one-sided Lipschitz differential inclusions
zbMATH Open document ID: 1121.34018
author: Grzegorz Gabor
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-02-19T00:00:00Z
review text: The author studies the following multivalued Cauchy problem \[ \dot{x}(t) \in F(x(t)),\quad a.e. \quad t\in I,\quad x(0)=x_0, \eqno(1) \] where \(I=[0,+\infty)\) and \(F:E\to 2^E\) is a multifunction with nonempty, convex and compact values in a Banach space \(E\) with a uniformly convex dual. By assuming that \(F\) is one-sided Lipschitz continuous and it has a sublinear growth, the author proves the existence of a continuous selection of the solution map, which is the multifunction that to every \(x_0 \in E\) assigns the set of all solutions to problem (1). In the last part of the paper, as an application, the problem of the existence of a viable trajectories, in a prescribed closed subset of \(E\), is studied.
reviewed by: Francesca Papalini
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 5128005
zbMATH Keywords: Differential inclusions
zbMATH Keywords: one-sided Lipschitz multivalued map
zbMATH Keywords: continuous selections
zbMATH Keywords: exit set
zbMATH Keywords: viability
zbMATH Keywords: Wazewski's retract method
zbMATH Keywords: strong deformation retracts
zbMATH Keywords: positive invariance
MaRDI profile type: Publication
full work available at URL: j.na.2005.12.038
OpenAlex ID: W2028018907
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DOI: 10.1016/J.NA.2005.12.038
description: scientific article; zbMATH DE number 5128005