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随机积分和微分方程解的存在性准则

丁协平

丁协平. 随机积分和微分方程解的存在性准则[J]. 应用数学和力学, 1985, 6(3): 265-270.
引用本文: 丁协平. 随机积分和微分方程解的存在性准则[J]. 应用数学和力学, 1985, 6(3): 265-270.
Ding Xie-ping. Criteria for the Existence of Solutions to Random Integral and Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(3): 265-270.
Citation: Ding Xie-ping. Criteria for the Existence of Solutions to Random Integral and Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(3): 265-270.

随机积分和微分方程解的存在性准则

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

  • 摘要: 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Lakshmikantham[3,4],Vaugham[2],De Blasi和Myjak[5]等人的结果.
  • [1] 丁协平,一般随机不动点定理及其应用,应用数学和力学,5,5(1984),699-708
    [2] Lakshmikantham V.,In Volterra Integral Equations,Springer-Verlag,737(1979),120-126.
    [3] Vaughn,R.L.,Existence and comparison results for nonlinear Volterra integnal equations in a Banach space,Appl.Analysis,7(1978),337-348.
    [4] Vaughn.R.L.,In Nonlinear Equations in Abstract Spaces,Academic Press,New York(1978),463-468.
    [5] 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.
    [6] Bharucha-Reid,A.T.,Random Integral Equations,Academic Press,New York(1972).
    [7] Tsokos,C.J and W.J.Padgett,Random Integral Equations with Applications to Life Sciences and Engineering,Academic Press,New York(1974).
    [8] Engl,H.W.A general stochastic fixed-point theorem for continuous random operators on stochastic domains,J.Math.Anal.Appl.,66(1978).220-231.
    [9] Engl,H.W.Random fixed point theorems,in Nonlinear Equations in Abstract Spaces.Academic Press,New York,(1978),67-80.
    [10] Bocsan,Gh.,A general random fixed point theorem and application to random equations,Rev.Roum.Math.Pures et.Appl.,26(3)(1981),375-379.
    [11] Himmelberg C.J.,Measurable relations,Fund Math.87(1975),53-72.
    [12] Castaing,C.and M.Valadier.,Convex Analysis and Measurable Multifunctions,Springer-Verlag 580(1977).
    [13] Lakshmikantham,V.and S.Leela,Nonlinear Differential Equations in Abstract Spaces.Pergamon Press,New York(1981).
    [14] Rus I.A.,On a theoremof Eisenfeld-Lakshmikantham,Nonlinear Anal.,TMA.,7(3)(1983),279-281.
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出版历程
  • 收稿日期:  1984-01-24
  • 刊出日期:  1985-03-15

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