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Applied Mathematics and Mechanics

, Volume 18, Issue 8, pp 721–737 | Cite as

Solutions for a system of nonlinear random integral and differential equations under weak topology

  • Ding Xieping
  • Wang Fan
Article
  • 39 Downloads

Abstract

In this paper, 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 Ranach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.

Key words

system of nonlinear random Volterra integral equations random Cauchy problem extremal random solution comparison result weak topology in Banach space 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Ding Xieping
    • 1
  • Wang Fan
    • 2
  1. 1.Department of MathematicsSichuan Normal UniversityChengduP. R. China
  2. 2.Department of MathematicsNantong Teacher's CollegeNantongP. R. China

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