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

D. Bahuguna

 Department of Mathematics, Indian Institute of Technology Kanpur, Kanpur 208 016, India
Received 12 October 2003; Revised 22 May 2004

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.