Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 2, Pages 171-179
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 Katarzyna Kolodziej. 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.
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.