随机积分和微分方程解的存在性准则

在1]中我们已证明了一个一般的随机不动点定理并给出了某些应用,在本文中我们将给出该结果的进一步应用.首先证明了一随机Darbo不动点定理,然后利用此定理在紧性假设下给出了非线性随机Volterra积分方程和非线性随机微分方程Cauchy问题随机解的存在性准则.我们的定理改进和推广了Lakshmikantham3,4],Vaugham2],De Blasi和Myjak5]等人的结果.

Criteria for the Existence of Solutions to Random Integral and Differential Equations

In 1], we proved a general rondom fixed point theorem and gave some applications. In this paper, we shall give further applications of the theorem. We first obtain a rondom Darbo's fixed point theorem, using the theorem, we give the criteria for the existence of solutions under compactness hypotheses to nonlinear rondom volterra integral equations and the Cauchy problem of nonlinear rondom differential equations. Our theorems improve andgeneralize some main results of Lakshmikanthem2], Vaughn3,4] as well as De Blasi and Myjak5].