Existence and approximation of solutions for discontinuous functional differential equations ✩

In this paper existence of solutions of initial value problems for discontinuous functional differential equations is investigated firstly. By applying the method of upper and lower solutions, which may be discontinuous, some existence results of extremal solutions are obtained. Furthermore, we also develop a monotone iterative technique for obtaining extremal solutions which are obtained as limits of monotone sequences.  2002 Elsevier Science (USA). All rights reserved.