On a mild solution of a semilinear functional-differential evolution nonlocal problem. (1997)

• Record Type: Journal Article
• Authors: Byszewski, Ludwik; Akca, Haydar
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 10:Number 3(1997)
• Page Start: 265
• Page End: 271
• Publication Date: 1997
• Subjects: abstract Cauchy problem -- evolution equation -- functional-differential equation -- nonlocal condition -- mild solution -- existence and uniqueness of the solution -- continuous dependence of the solution -- a C0 semigroup -- the Banach contraction theorem; 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/S1048953397000336
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : The existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear functional-differential evolution equation in a general Banach space are studied. Methods of a C 0 semigroup of operators and the Banach contraction theorem are applied. The result obtained herein is a generalization and continuation of those reported in references [2-8].