On a nonlocal Cauchy problem for differential inclusions
type: Item
instance of: scholarly article
title: On a nonlocal Cauchy problem for differential inclusions
zbMATH Open document ID: 1080.34005
DOI: 10.1155/S108533750430610X
author: Efrosini P. Gatsori
author: Sotiris K. Ntouyas
author: Y. G. Sficas
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/52042
review text: The paper concerns a system which consists of the differential inclusion \[ y'(t)\in F(t,y(t)) \] and the nonlocal condition \[ y(0)+\sum_{k=1}^{p}c_ky(t_k)=y_0. \] Here, \(F:[0,b]\times \mathbb{R}^n\to \mathbb{R}^n\) is a certain Carathéodory multi-valued map, whereas \(0\leq t_1<\cdots<t_p\leq b\) and \(c_1\neq0\), \dots, \(c_p\neq0\). In contrast with the paper by \textit{M.~Benchohra} and \textit{S.~K.~Ntouyas} [Georgian Math.~J. 7, 221--230 (2000; Zbl 0960.34049)], the \(F\)-values are not necessarily convex. Using either the Covitz-Nadler fixed-point theorem or the Bressan-Colombo selection theorem combined with Schaefer's fixed-point theorem, there are derived two distinct results which state the existence of solutions to the system above.
reviewed by: Corneliu Ursescu
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 2163663
zbMATH Keywords: differential inclusion
zbMATH Keywords: nonlocal Cauchy problem
MaRDI profile type: Publication
OpenAlex ID: W1980013819
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description: scientific article; zbMATH DE number 2163663