非线性随机积分和微分方程组的解<sup>*</sup>

非线性随机积分和微分方程组的解^*

基金项目: * 国家自然科学基金

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

摘要: 在本文中我们首先对具有随机定义域的连续随机算子组证明了Darbao型不动点定理。应用此定理我们给出了非线性随机Volterra积分方程组和非线性随机微分方程组的Cauchy问题解的存在性准则。这些随机方程组的极值随机解的存在性和随机比较结果也被获得。我们的定理改进和推广Tyaughn,Lakshmikantham,Lakshmikantham-Leela,DeBlast-Myjak和第一作者的相应结果。
- 非线性积分方程 /
- 随机Volterra积分方程 /
- 随机Cauchy问题 /
- 极值随机解 /
- 比较结果
Abstract: In this paper we first prove a Darbao type fixed point theorem for a system of continuous random operators with random domains. Thenb, by using the theorem. wegive the existence criteria of solutions for a systems of nonlinear random volterraintegral equations and for the Cauchy problem of a system of nonlinear random differential equations. The existence of extremal random solutions and random comparison results for these systems of random equations are also obtained our theorems improve and generalize the corresponding results of Vaughn Lakshmikantham Lakshmidantham-Leela De blasi-Myjak and Ding.
- nonlinear Integral equations /
- random Voltcrra integral equations /
- random Cauchy problem /
- extremal random solution /
- comparison result

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