Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 3, Pages 265-271

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

Copyright © 1997 Ludwik Byszewski and Haydar Akca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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].