Stability of solution sets of differential equations with multivalued right-hand side
type: Item
instance of: scholarly article
title: Stability of solution sets of differential equations with multivalued right-hand side
zbMATH Open document ID: 0808.34013
author: A. Constantin
published in: Journal of Differential Equations
publication date: 1995-03-15T00:00:00Z
review text: The following initial value problem in \(\mathbb{R}^ n\) for a differential inclusion is considered: \(x'(t) \in F(t,x(t))\), \(x(0) = b\). It is assumed that \(F\) is continuous with convex and compact values and \(D(F(t,x)\), \(F(t,y)) \leq k(t) | x - y |\) with a continuous function \(k (D(A,B)\) stands for the Hausdorff distance of the sets \(A,B)\). Then it is proved that the map \(S\) which associates to every initial condition \(b \in \mathbb{R}^ n\) the solution set of the above differential inclusion is continuous from \(\mathbb{R}^ n\) to the space of all continuous maps \(x : \mathbb{R}_ + \to \mathbb{R}^ n\) such that \(x(t)/g(t)\) is bounded on \(\mathbb{R}_ +\), where \(g(t) = \exp (2 \int^ t_ 0 k(s)ds)\).
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 696889
zbMATH Keywords: continuous
zbMATH Keywords: dependence on initial condition
zbMATH Keywords: initial value problem
zbMATH Keywords: differential inclusion
reviewed by: Vlastimil Křivan
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1149
OpenAlex ID: W1967948745
Wikidata QID: Q58870122
DOI: 10.1006/JDEQ.1994.1149
description: scientific article; zbMATH DE number 696889