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随机积分和微分方程在弱拓扑下解的存在性和比较结果*

丁协平

丁协平. 随机积分和微分方程在弱拓扑下解的存在性和比较结果*[J]. 应用数学和力学, 1987, 8(12): 1039-1050.
引用本文: 丁协平. 随机积分和微分方程在弱拓扑下解的存在性和比较结果*[J]. 应用数学和力学, 1987, 8(12): 1039-1050.
Ding Xie-ping. Existence and Comparison Results of Solutions for Nonlinear Random Integral and Differential Equations Relative to Weak Topology[J]. Applied Mathematics and Mechanics, 1987, 8(12): 1039-1050.
Citation: Ding Xie-ping. Existence and Comparison Results of Solutions for Nonlinear Random Integral and Differential Equations Relative to Weak Topology[J]. Applied Mathematics and Mechanics, 1987, 8(12): 1039-1050.

随机积分和微分方程在弱拓扑下解的存在性和比较结果*

基金项目: * 中国科学院科学基金资助的课题

Existence and Comparison Results of Solutions for Nonlinear Random Integral and Differential Equations Relative to Weak Topology

  • 摘要: 在本文中,我们对非线性随机Volterra积分方程在Banach空间的弱拓扑下的随机解证明了几个存在定理.然后作为应用,我们得到了随机微分方程的弱随机解的存在定理.还得到了这些随机方程的极值随机解的存在性和随机比较定理.我们的定理改进和推广了[4,5,10,11,12]中的相应结果.
  • [1] Vaughn,R.L.,Existence and comparison results for nonlinear Volterra integral equations in Banach spaces,Appl.Anal.,7(1978),337-348.
    [2] Vaughn,R.L.,Criteria for the existence and comparison of solutions to nonlinear Volterra integral equations in Banach spaces,in Nonlinear Equations in Abstract Spaces,Acad.Press,New York(1978),463-468.
    [3] Lakshmikantham,V.,Existence and comparison results for Volterra integral equations in Banach spaces,in:Volterra Integral Equations,Springer-Verlag,737(1979),120-126.
    [4] Lakshmikantham,V.and S.Leela,Nonlinear Differential Equations in Abstract Spaces,Pergamon Press,New York(1981).
    [5] Mitchell,A.R.and C.Smith,An existence theorem for weak solutions of differential equations in Banach spaces,in:Nonlinear Equations in Abstract Spaces,Acad.Press,New York(1978),387-403.
    [6] Bharucha-Reid,A.T.,Random Integral Equations.Acad.Press,New York(1972).
    [7] Tsokos,C.J.and W.J.Padgett,Random Integral Equations with Applications to Life Science and Engineering,Acad.Press,New York(1974).
    [8] 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),265-270
    [9] 丁协平,随机积分方程和微分方程解的存在性和比较结果,应用数学和力学,7,7(1986),597-604
    [10] Ding Xie-ping,A general random fixed point theorem of weak continuous random operators and its applications.(to appear).
    [11] Cramer,E.J.,V.Lakshmikantham and A.R.Mitchell,On the existence of weak solutions of differential equations in nonreflexive Banach spaces,Nonlinear Anal.,2(1978),169-177.
    [12] Szep,A.,Existence theorem for weak solutions of ordinary differential equations in reflexive Banach spaces,Studia Scientiarum Math.Hungrica,6(1971),197-203.
    [13] Castaing,C.and M.Valadier,Convex Analysis and Measurable Multifunctions,Springer Verlag(1977),580.
    [14] De Blasi,F.S.and J.Myjak,Random differential equations on closed subsets of Banach spaces,J.Math.Anal.Appl.,90(1982),273-285.
    [15] Hille,E.and R.S.Phillips,Functional Analysis and Semi-Groups,Amer.Math.Soc.,Providence,Rhode Island(1957).
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出版历程
  • 收稿日期:  1986-07-26
  • 刊出日期:  1987-12-15

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