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弱拓扑下的非线性随机积分和微分方程组的解*

丁协平 王凡

丁协平, 王凡. 弱拓扑下的非线性随机积分和微分方程组的解*[J]. 应用数学和力学, 1997, 18(8): 669-684.
引用本文: 丁协平, 王凡. 弱拓扑下的非线性随机积分和微分方程组的解*[J]. 应用数学和力学, 1997, 18(8): 669-684.
Ding Xieping, Wang Fan. Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology[J]. Applied Mathematics and Mechanics, 1997, 18(8): 669-684.
Citation: Ding Xieping, Wang Fan. Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology[J]. Applied Mathematics and Mechanics, 1997, 18(8): 669-684.

弱拓扑下的非线性随机积分和微分方程组的解*

基金项目: * 国家自然科学基金

Solutions for a System of Nonlinear Random Integral and Differential Equations under Weak Topology

  • 摘要: 在本文中,我们首先对具有随机定义域的弱连续随机算子组证明了一个Darbo型随机不动点定理.利用这一定理,我们对Banach空间中关于弱拓扑的非线性随机Volterra积分方程组给出了随机解的存在性准则.作为应用,我们得到了非线性随机微分方程组的Canchy问题弱随机解的存在定理.也得到了这些随机方程组在Banach空间中关于弱拓扑的极值随机解的存在性和随机比较结果.我们的定理改进和推广了Szep,Mitchell-Smith,Cramer-Lakshmikantham,Lakshmikantham-Leela和丁的相应结果.
  • [1] A. T. Bharucha-Reid, Random Integral Equations, Acad. Press, New York (1972).
    [2] C. Castaing and. M. Valadier, Convex Analysis and Measurable Multifunctions, Springer-Verlag (1977), 580.
    [3] E. J. Cramer, V. Lakshmikantham and A. R. Mitchell, On the existence of weaksolutions of differential equations in nonreflexive Banach spaces, Nonlinear Anal., 2(1978), 169~177.
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    [5] 丁协平.随机集值映射的不动点定理及其应用,应用数学和力学,5(4) (1984), 561-576,
    [6] X, P, Ding, Existence, uniqueness and approximation of solutioas for a system of nonlinear ra mdom operator equations,Nonlinear Anal,a(6)(1984),563-576,
    [7] 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,g(3) (1985), 265-270,
    [8] 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.
    [9] 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,应用数学和力学, 8(12),(1987),1039-1050,
    [10] Ding Xieping, Solutions for a system of random Qperator equations and someapplications, Scientia Sinica, 30, 8 (1987), 785~795.
    [11] Ding Xieping, A general random fixed point theorem of weakly continuous randomoperator with applications, J. Engineering Math., 5, 2 (1988), 1~7.
    [12] E. Hille and R. S. Phillips, Ftnctional Analvsis and Semi-Groups, Amer. Math. Soc.Providence, RI (1957).
    [13] V. Lakshmikantham, Existence and comparison results for Volterra integral equations inBanach spaces, Volterra Intngral Equations, Springer-Verlag, 737 (1979), 120~126.
    [14] V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces,Pergamon Press, New York (1981).
    [15] A. R. Mitchell and C. Smith, An existence theorem for weak solutions of differentialequations in Banach spaces, Nonlinear Equalions in Abstract Spaces, Acad. Press, NewYork (1978), 387~403.
    [16] A. Szep, Existence theorem for weak solutions of ordinary differential equations inrenexive Banach spaces, studta sci. MaIh. Himgica, 6 (1971), 197~203.
    [17] C. J. Tsokos and W. J. Padgett, Random Integral Equations with Applications to LifeScience and Engineering, Acad. Press, New York (1974).
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    [19] R. L. Vaughn, Criteria for the existence and comparison of solutions to nonlinearVolterra integral equations in Banach spaces, Nonlinear Equations in Abstract Spaces.Acad. Press. New York (1978), 463~468.
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出版历程
  • 收稿日期:  1996-12-22
  • 刊出日期:  1997-08-15

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