On the set of solutions of the Cauchy problem in Banach spaces
type: Item
instance of: scholarly article
title: On the set of solutions of the Cauchy problem in Banach spaces
zbMATH Open document ID: 0804.34054
DOI: 10.1007/BF01189827
author: Mieczysław Cichoń
author: Ireneusz Kubiaczyk
published in: Archiv der Mathematik
publication date: 1994-11-13T00:00:00Z
review text: This paper contains some Kneser type theorems for an abstract Cauchy problem \(x'= f(t,x)\), \(x(0)= x_ 0\) in an infinite-dimensional Banach space \(E\). A function \(f\) is assumed to satisfy Carathéodory-type conditions with respect to the weak topology on \(E\). However, some compactness conditions expressed in terms of a measure of weak noncompactness is assumed. Under the assumptions mentioned above a nonemptiness, compactness and connectedness of the set of all pseudo- solutions for the Cauchy problem is proved. Topological properties of this set are considered in the space \(C(J,E)\) with its weak topology.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 687043
zbMATH Keywords: Pettis integral
zbMATH Keywords: Kneser type theorems
zbMATH Keywords: abstract Cauchy problem
zbMATH Keywords: Banach space
zbMATH Keywords: Carathéodory-type conditions
zbMATH Keywords: measure of weak noncompactness
zbMATH Keywords: pseudo-solutions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01189827
OpenAlex ID: W2089031580
description: scientific article; zbMATH DE number 687043