Solutions for a system of nonlinear random integral and differential equations

Abstract

In this paper, we first prove a Darbao type fixed point theorem for a system of continuous random operators with random domains. Then, by using the theorem, we give the existence criteria of solutions for a systems of nonlinear random Volterra integral equations and for the Cauchy problem of a system of nonlinear random differential equations. The existence of extremal random solutions and random comparison results for these systems of random equations are also obtained. Our theorems improve and generalize the corresponding results of Vaughn, Lakshmikantham, Lakshmikantham-Leela, De Blasi-Myjak and Ding.