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
Cracow University of Technology, Institute of Mathematics, Warszawska 24, Cracow 31-155, Poland
Received 1 November 1997; Revised 1 April 1998
Copyright © 1999 Ludwik Byszewski. 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.