Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 2, Pages 181-194

Exact and approximate solutions of delay differential equations with nonlocal history conditions

S. Agarwal and D. Bahuguna

Department of Mathematics, Indian Institute of Technology, Kanpur 208 016, India

Received 28 April 2004; Revised 23 July 2004

Copyright © 2005 S. Agarwal and 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.


We study the exact and approximate solutions of a delay differential equation with various types of nonlocal history conditions. We establish the existence and uniqueness of mild, strong, and classical solutions for a class of such problems using the method of semidiscretization in time. We also establish a result concerning the global existence of solutions. Finally, we consider some examples and discuss their exact and approximate solutions.