非线性随机积分和微分方程组的解  

Solutions for a System of Nonlinear Random Integral and Differential Equations

作　　者：丁协平[1] 王凡 

机构地区：[1]四川师范大学数学系,南通师范专科学校数学系

出　　处：《应用数学和力学》1996年第6期471-481,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金

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．In this paper, we first prove a Darbao type fixed point theorem for a system of continuous random operators with random domains. Then, by using the theorem, we give the existence criteria of solutions for a systems of nonlinear random Volterra integral 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 correponding results of Vaughn.Lakshmikantham, Lakshmikantham-Leela, De Blasi-Myjak and Ding.

关 键 词：非线性 随机积分方程 随机微分方程 解 存在性 

分 类 号：O211.63[理学—概率论与数理统计]