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Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 171-179
http://dx.doi.org/10.1155/S1048953300000186

Existence and uniqueness of solutions of a semilinear functional-differential evolution nonlocal Cauchy problem

Cracow University of Technology, Institute of Mathematics, Warszawska 24, Cracow 31-155, Poland

Received 1 December 1998; Revised 1 April 1999

Copyright © 2000 Hindawi Publishing Corporation. 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.

Abstract

Two theorems about the existence and uniqueness of mild and classical solutions of a semilinear functional-differential evolution nonlocal Cauchy problem in a general Banach space are proved. Methods of semigroups and the Banach contraction theorem are applied.