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Banach空间中二阶微分方程的无穷边值问题 被引量：2

Infinite Boundary Value Problems for Second Order Differential Equations in Banach Space
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摘要 利用M¨onch不动点定理研究了Banach空间中一类无穷区间上的二阶微分方程的边值问题,在比较弱的条件下得到了解的存在性。 The Mnch fixed point theorem is used to study a kind of infinite boundary value problems for second order differential equations in a Banach space. The existence of solutions is also obtained under weaker conditions.
作者 刘衍胜
机构地区 山东师范大学数学系
出处 《工程数学学报》 CSCD 北大核心 2003年第2期99-107,共9页 Chinese Journal of Engineering Mathematics
基金 国家自然科学基金资助项目(10171057) 山东省中青年科学家奖励基金项目.
关键词 不动点 边值问题 无穷区间 二阶微分方程 fixed point boundary value problem infinite interval
分类号 O175.8 [理学—基础数学]
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参考文献6

  • 1Lakshndkantham V, Leela S. Nonlinear differential equations in abstract space[M]. Pergamon Oxford,1981.
  • 2Deinding K. Nonlinear functional analysis[M]. Berlin: Springer-Verlag,1985.
  • 3Guo D J, Lakshmikantham V. Nonlinear problems in abstract cones[ M ]. New York: Academic Press lnc, 1988.
  • 4Liu L S. Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordeled Banach spaces[J]. Indian J Pure Appl Math, 1996 ;27:959- 972.
  • 5Guo D J, Lakshmikantham V, Liu X Z. Nonlinear integral equations in abstract spaces[M]. Kluwer Academic Publishers, 1996.
  • 6Guo D J. Boundary value problems for impulsive integro-differential equation on unbounded domains in a Banach space[ J ]. Applied Mathematics and Computation, 1999; 99:1 - 15.

同被引文献13

  • 1宋玉霞,闫宝强.一类脉冲微分方程三点边值问题的比较定理[J].科学技术与工程,2005,5(15):1051-1052. 被引量：1
  • 2[1]Liu X.Iterative methods for solutions of impulsive functional differential systems.Appl Anal,1992 ;44:171-182
  • 3[2]Zhang F,Ma Z,Yan J.Periodic boundary value problems and monotone iterative methods for first order impulsive differential equations with delay.Indian J Pure Appl Math,2001 ;32:1695-1707
  • 4[5]Guo Dajun.Impulsive integral-differential equations in Banach spaces and applications.Appl Math Stochastic Anal,1992;5:111-122
  • 5[6]Guo Dajun.Boundary value problems for impulsive integro-differential equation on unbounded domains in a Banach space.Applied Mathematics and Computation,1999 ;99:1 -15
  • 6[8]郭大钧.非线性泛函分析.济南:山东科技出版社,2003
  • 7[9]Guo Dajun,Lakshmikantham V,liu Xinzhi,Nonlinear integral equations in Abstract Spaces.Dordrecht:Kluwer Academic Publishers,1996
  • 8Guo Dajun.Boundary value problems for impulsive integro-diflFerential equations on unbounded domains in a Banach space[J].Appl Math Comput,1999,99:1-15.
  • 9Liu Yansheng.Existence and unboundedness of positive solutions for singular boundary value problems on half-line[J].Appl.Math.Comput,2003,144:543-556.
  • 10Guo Dajun,Lakshmikantham V.Liu Xinzhi.Nonlinear Integral Equations in Abstract Spaces[M].Kluwer Academic Publishers,1996.

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工程数学学报
2003年 第2期

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