Table of Contents
Journal of Applied Mathematics and Stochastic Analysis
Volume 12, Issue 1, Pages 91-97
http://dx.doi.org/10.1155/S1048953399000088

Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem

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

Received 1 November 1997; Revised 1 April 1998

Copyright © 1999 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

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.