Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology

Ding Xieping; Wang Fan

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Ding Xieping, Wang Fan. Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology[J]. Applied Mathematics and Mechanics, 1997, 18(8): 669-684.

Citation:

Ding Xieping, Wang Fan. Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology[J]. Applied Mathematics and Mechanics, 1997, 18(8): 669-684.

Citation:

Ding Xieping, Wang Fan. Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology[J]. Applied Mathematics and Mechanics, 1997, 18(8): 669-684.

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Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology

Ding Xieping¹,
Wang Fan²

1.
Department of Mathematics, Sichuan Normal University Chengdu, Sichuan 610066, P. R. China;
2.
Department of Mathematics, Nantong Teacher's College, Nontong, Jiangsu 226007, P. R. China

Received Date: 1996-12-22
Publish Date: 1997-08-15

Abstract

Abstract

In this paper, a Darbao type random fired point theorem for a system of lveak continuous random operators with random domain is first proved Then, by using thetheorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces aregiven. As applications, some existence theorems of weak random sohttions for the random Cauchy problem of a system of nonlinear random differential equations areobtained, as well as the existence of extremal random solutions and random comparison resultsfor these systems of random equations relative to weak topotogy in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are mproved and generalized bythese theorems.
- system of nonlinear random Volterra integral equations,
- random Cauchy problem,
- extremal random solution,
- comparison result,
- weak topology in Banach space

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References(19)

References

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