Journal of Applied Mathematics and Stochastic Analysis 
Volume 12 (1999), Issue 1, Pages 91-97
doi:10.1155/S1048953399000088

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

Ludwik Byszewski

 Cracow University of Technology, Institute of Mathematics, Warszawska 24, Cracow 31-155, Poland
Received 1 November 1997; Revised 1 April 1998

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.