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.

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

  • Received Date: 1986-07-26
  • Publish Date: 1987-12-15
  • In this paper, we prove several existence theorems of random solutions to nonlinear random Volterra integral equations under the weak topology of Banach spaces. Then, as applications, we obtain the existence theorems of weak random solutions to random differential equations. Existence of extremal random solutions and a random comparison theorem for these random equations are also obtained. Our theorems improve and extend the corresponding results in [4,5,10,11,12].
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  • [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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