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Banach空间非线性脉冲Volterra积分方程组的整体解

陈芳启 陈予恕

陈芳启, 陈予恕. Banach空间非线性脉冲Volterra积分方程组的整体解[J]. 应用数学和力学, 2001, 22(6): 551-560.
引用本文: 陈芳启, 陈予恕. Banach空间非线性脉冲Volterra积分方程组的整体解[J]. 应用数学和力学, 2001, 22(6): 551-560.
CHEN Fang-qi, CHEN Yu-shu. Global Solutions of Systems of Nonlinear Impulsive Volterra Integral Equations in Banach Spaces[J]. Applied Mathematics and Mechanics, 2001, 22(6): 551-560.
Citation: CHEN Fang-qi, CHEN Yu-shu. Global Solutions of Systems of Nonlinear Impulsive Volterra Integral Equations in Banach Spaces[J]. Applied Mathematics and Mechanics, 2001, 22(6): 551-560.

Banach空间非线性脉冲Volterra积分方程组的整体解

基金项目: 国家自然科学基金资助重大项目(19990510);国家教委博士点专项基金资助项目(D09901)
详细信息
    作者简介:

    陈芳启(1963- ),男,山东人,博士,已发表论文30余篇.

  • 中图分类号: O177.91

Global Solutions of Systems of Nonlinear Impulsive Volterra Integral Equations in Banach Spaces

  • 摘要: 研究Banach空间中定义在无穷区间R+上具有无穷多个脉冲点的非线性脉冲Volterra积分方程组解的存在性。给出了若干极值解的存在定理,改进了定义在有限区间上具有有限个脉冲点情形时该类方程的相应结果,并利用该结果讨论了一个无穷维积分方程组。
  • [1] Lakshimikantham V, Bainov D D, Simeonov P S. Theory of Impulsive Differential Equations[M]. Singapore: World Scientific,1 989.
    [2] GUO Da-jun. Nonlinear impulsive Volterra integral equations in Banach spaces and applications[J]. J Appl Math Stochastic Anal,1993,6(1):35-48.
    [3] GUO Da-jun, Lakshimikantham V. Nonlinear Problems in Abstract Cones[M]. Boston and New York: Academic Press Inc,1988.
    [4] GUO Da-jun. Impulsive integral equations in Banach spaces and applications[J]. J Appl Math Stochastic Anal,1992,5(2):111-1 22.
    [5] Martin R H. Nonlinear Operators and Differential Equations in Banach Space[M]. New York: J Wiley and Sons,1976.
    [6] Heinz H P. On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions[J]. Nonlinear Anal,1983,7(12):1351-1371.
    [7] GUO Da-jun. Extremal solutions of nonlinear Fredholm integral equations in Banach spaces[J]. Northeastern Math J,1991,7(4): 416-423.
    [8] Vaughn R L. Existence and comparison results for nonlinear Volterr a integral equations in a Banach space[J]. Appl Anal,1978,7(2):337-348.
    [9] CHEN Fang-qi. Existence of solutions for mixed monotone impulsive Volterra integral equations in Banach spaces[J]. Acta Math Scientia,1998, 18(4):371-378.
    [10] 陈芳启. Banach空间混合单调脉冲微分积分方程解的存在性[J]. 系统科学与数学,1999,19(1):111-115.
    [11] Deimling K. Nonlinear Functional Analysis[M]. Berlin: Sprin ger-Verlag,1985.
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出版历程
  • 收稿日期:  1999-11-01
  • 修回日期:  2000-11-23
  • 刊出日期:  2001-06-15

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