Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem. (1999)

• Record Type: Journal Article
• Authors: Byszewski, Ludwik
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 12:Number 1(1999)
• Page Start: 91
• Page End: 97
• Publication Date: 1999
• Subjects: abstract Cauchy problem -- ordinary functional-differential equation -- nonlocal condition -- existence and uniqueness of a classical solution -- mild solution -- Banach contraction theorem -- Picard method; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953399000088
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem in a general Banach space. For this purpose, a special kind of a mild solution is introduced and the Banach contraction theorem and a modified Picard method are applied.