Nonlocal Cauchy problem for delay integrodifferential equations of Sobolev type in Banach spaces
type: Item
instance of: scholarly article
title: Nonlocal Cauchy problem for delay integrodifferential equations of Sobolev type in Banach spaces
zbMATH Open document ID: 1028.45006
DOI: 10.1016/S0893-9659(02)00052-6
author: M. Chandrasekaran
author: Krishnan Balachandran
author: Jong Yeoul Park
published in: Applied Mathematics Letters
publication date: 2003-03-10T00:00:00Z
review text: \textit{L. Byszewski} established the existence and uniqueness of mild, strong, and classical solutions of the nonlocal Cauchy problem [J. Math. Anal. Appl. 162, 494-505 (1991; Zbl 0748.34040)] and investigated the same problem for different types of evolution equations in Banach spaces in a joint paper with \textit{H. Akca} [J. Appl. Math. Stochastic Anal. 10, 265-271 (1997; Zbl 1043.34504)]. \textit{H. Brill} investigated the existence of solutions for a semilinear Sobolev evolution equation in a Banach space [J. Differ. Equations 24, 412-425 (1977; Zbl 0346.34046)]. Recently, \textit{K. Balachandran, D. G. Park} and \textit{Y. C. Kwun} discussed the problem for nonlinear integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces [Commun. Korean Math. Soc. 14, 223-231 (1999; Zbl 0972.45009)]. In this paper, the authors prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. They obtain the results by using the theory of compact semigroups and Schaefer's fixed-point theorem.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 1878891
zbMATH Keywords: nonlocal Cauchy problem
zbMATH Keywords: nonlocal conditions
zbMATH Keywords: mild and strong solutions
zbMATH Keywords: time varying delay integrodifferential equations of Sobolev type
zbMATH Keywords: Banach spaces
zbMATH Keywords: compact semigroups
zbMATH Keywords: Schaefer's fixed-point theorem
MaRDI profile type: Publication
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full work available at URL: s0893-9659(02)00052-6
OpenAlex ID: W1990559355
description: scientific article; zbMATH DE number 1878891