Topological structure of solution sets to multi-valued asymptotic problems
type: Item
instance of: scholarly article
title: Topological structure of solution sets to multi-valued asymptotic problems
zbMATH Open document ID: 0974.34045
DOI: 10.4171/ZAA/937
author: Jan Andres
author: Grzegorz Gabor
author: Lech Górniewicz
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2001-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/48980
review text: It is considered the Cauchy problem \[ \dot{x}(t)\in F(t,x(t)),\quad x(0)=x_{0}, \tag{1} \] with \(t\in J= [0,\infty),\) and \(F:J\times \mathbb{R}^{n}\mapsto \mathbb{R}^{n}\) is a set-valued map with nonempty, compact values, \(F(\cdot,x)\) is measurable for all \(x\in \mathbb{R}^{n}\) and there exists a locally integrable function \(\eta:J\to J\) such that, for every \(t\in J\) and all \(x,y \in \mathbb{R}^{n}, d_{H}(F(t,x),F(t,y))\leq \eta(t)|x-y|\). Here, \(d_{H}\) stands for Hausdorff distance. The topological structure of a solution set to problem (1) is studied. In particular, if \(\int_{0}^{\infty}\eta(t) dt<\infty\) then the existence of an entirely bounded solution on \(J\) is proved.
Mathematics Subject Classification ID: 34C30
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 1453203
zbMATH Keywords: solution sets
zbMATH Keywords: acyclicity
zbMATH Keywords: asymptotic problems
zbMATH Keywords: differential inclusions
zbMATH Keywords: discontinuous autonomous inclusions
zbMATH Keywords: inverse systems
zbMATH Keywords: essential operators
MaRDI profile type: Publication
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OpenAlex ID: W2030126934
description: scientific article; zbMATH DE number 1453203