Journal of Applied Mathematics and Stochastic Analysis 
Volume 10 (1997), Issue 3, Pages 265-271
doi:10.1155/S1048953397000336

On a mild solution of a semilinear functional-differential evolution nonlocal problem

Ludwik Byszewski1 and Haydar Akca2

 1Cracow University of Technology, Institute of Mathematics, Warszawska 24, Cracow 31-155, Poland
2Akdeniz University, Department of Mathematics, Antalya 0720, Turkey
Received 1 February 1997; Revised 1 May 1997

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 C0 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].