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

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

Katarzyna Kolodziej

 Cracow University of Technology, Institute of Mathematics, Warszawska 24, Cracow 31-155, Poland
Received 1 December 1998; Revised 1 April 1999

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.