Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 3, Pages 213-219
doi:10.1155/S1048953304310026
Existence, uniqueness, and regularity of solutions to semilinear retarded differential equations
Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur 208 016, India
Received 12 October 2003; Revised 22 May 2004
Copyright © 2004 D. Bahuguna. 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
In the present work, we consider a semilinear retarded differential equation in a Banach space. We first establish the existence and uniqueness of a mild solution and then prove its regularity under different additional conditions. Finally, we consider some applications of the abstract results.