随机积分方程和微分方程解的存在性和比较结果
Existence and Comparison Results for Solutions’ of Random Integral and Differential Equations
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摘要: 本文是[1]的继续.在本文中我们对非线性随机Volterra积分方程给出了解的另一存在性准则,极值解的存在性定理和随机积分不等式的比较定理,这些定理分别推广了Vaughan[2,3]和Lakshmikantham[4,5]的相应结果.Abstract: This paper is the continuation of [1]. In this paper, we give another criteria of the existence of solutions for nonlinear random Volterra integral. A comparison theorem and the existence of random extremal solutions are also obtained by using the notion of ordering with respect to a cone. Our theorems generalize the corresponding results of Vaughan[2,3] and Lakshmikantham[4,5].
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[1] 丁协平,随机积分和微分方程解的存在性准则,应用数学和力学.6,3(1985). [2] Vaughan,R.L.,Existence and comparison results for nonlinear Volterra integral equations in Banach spaces.Appl.Anal.7(1978),337-348. [3] Vaughan,R.L.,Criteria for the existence and comparison of solutions to nonlinear Volterra integral equations in Banach spaces,Nonlinear Equations in Abstract Spaces,Acad.Press,New York(1978),463-468. [4] Lakshmikantham V.,Existence and comparison results for Volterra integral equations in Banach spaces,Volterra Integral Equations,Springer-Verlag,737(1979),120-126. [5] Lakshmikantham V.and S.Leela,Nonlinear Differential Equations in Abstract Spaces,Pergamon Press,New York(1981). [6] De Blasi F.S.and J.Myjak,Random differential equations on closed subsets of a Banach space.J.Math.Anal Appl.90(1982),273-285. -
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