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Solutions for a system of nonlinear random integral and differential equations under weak topology. (English) Zbl 0912.60079

Summary: A Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. Then, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.

MSC:

60H20 Stochastic integral equations
47H40 Random nonlinear operators
45D05 Volterra integral equations
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References:

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