Existence and comparison results for solutions of random integral and differential equations (Q1083766)

This paper is the continuation of the author's paper, ibid. 6, 269-275 (1985; Zbl 0578.60058). In this paper, we give another criterion for the existence of solutions of the nonlinear random Volterra integral. A comparison theorem and the existence of random extremal solutions are also obtained by using the notion of ordering with respect to a cone. Our theorems generalize the corresponding results of \textit{R. L. Vaughn} [Appl. Anal. 7, 337-348 (1978; Zbl 0403.45023) and Nonlinear equations in abstract spaces, Proc. int. Symp., Arlington 1977, 463-468 (1978; Zbl 0439.45022)] and \textit{V. Lakshmikantham} [Lect. Notes Math. 737, 120-126 (1979; Zbl 0418.45015)] and \textit{V. Lakshmikantham} and \textit{S. Leela} [Nonlinear differential equations in abstract spaces. (1981; Zbl 0456.34002)].