Existence of Extremal Solutions of Differential Equations with Delay in Banach Spaces

Abstract

: In this paper, by using the monotone iterative method and Daher's fixed point theorem and an inequality of noncompact measure of Monch and Von Harten, we study the existence of maximum solution and minimal solution and the iterative approximation of the following initial value problem for O.D.E with delay in Banach spaces u’ = f(t, u(t), ut), ut0 = ψ0 and give a sufficient condition of the existence of solutions of the above problem. The obtained results improve and generalize the corresponding results