弱拓扑下的非线性随机积分和微分方程组的解<sup>*</sup>

丁协平; 王凡

弱拓扑下的非线性随机积分和微分方程组的解^*

丁协平¹,
王凡²

1.
四川师范大学数学系, 成都 610066;
2.
南通师范专科学校数学系, 南通 226007

基金项目: * 国家自然科学基金

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出版历程
- 收稿日期: 1996-12-22
- 刊出日期: 1997-08-15

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

摘要

摘要: 在本文中,我们首先对具有随机定义域的弱连续随机算子组证明了一个Darbo型随机不动点定理.利用这一定理,我们对Banach空间中关于弱拓扑的非线性随机Volterra积分方程组给出了随机解的存在性准则.作为应用,我们得到了非线性随机微分方程组的Canchy问题弱随机解的存在定理.也得到了这些随机方程组在Banach空间中关于弱拓扑的极值随机解的存在性和随机比较结果.我们的定理改进和推广了Szep,Mitchell－Smith,Cramer－Lakshmikantham,Lakshmikantham-Leela和丁的相应结果.
- 非线性随机Volterra积分 /
- 随机Cauchy问题 /
- 极值随机解 /
- 比较结果 /
- Banach空间中弱拓补
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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参考文献(19)

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