Existence Theorems for a Class of Functional Differential Systems

Abstract

**Please note that the full text is embargoed** ABSTRACT: In recent papers [2,6], the authors have established existence and comparison theorems for the well known Cauchy problem for ordinary differential equations without using the monotone property on the given system. These results are obtained under the conditions of the type which have been considered in the classical paper of Müller [8]. The interesting feature of the results established in [2,6], is the fact that the solutions of the Cauchy problem remain in the given sector. In this paper, we shall first establish existence and comparison theorems for a class of more general functional differential systems without using monotone property. Further we develop a monotone iterative technique to establish the existence of minimal and maximal solutions.