Criteria for the existence of solutions to random integral and differential equations

In1], we proved a general random fixed point theorem and gave some applications. In this paper, we shall give further applications of the theorem. We first obtain a random Darbo's fixed point theorem, using the theorem, we give the criteria for the existence of solutions under compactness hypotheses to nonlinear random volterra integral equations and the Cauchy problem of nonlinear random differential equations. Our theorems improve and generalize some main results of Lakshmikanthem²], Vaughn^3,4] as well as De Blasi and Myjak⁵].