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Banach空间中二阶非线性脉冲奇异微分方程多点无穷边值问题的正解 被引量：3

THE EXISTENCE OF POSITIVE SOLUTIONS FOR MULTIPOINT INFINITE BOUNDARY VALUE PROBLEMS OF SECOND ORDER NONLINEAR IMPULSIVE SINGULAR DIFFERENTIAL EQUATIONS IN BANACH SPACES
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摘要 利用锥理论和Mnch不动点定理结合单调迭代技巧,研究了Banach空间中一类二阶非线性脉冲奇异微分方程多点无穷边值问题,获得了正解的存在性定理和正解的迭代序列,改进和推广了某些已知结果. By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate multipoint infinite boundary value problems of second order nonlinear impulsive singular differential equations in Banach spaces and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results improve and generalize some existing results.
作者 李耀红 张晓燕
机构地区 宿州学院数学与统计学院 山东大学数学学院
出处 《系统科学与数学》 CSCD 北大核心 2011年第7期845-858,共14页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金项目(10701049) 安徽省高校省级优秀青年基金项目(2011SQRL153) 安徽省高校省级优秀人才基金项目(2011SQRL153 2010SQRL195)
关键词 脉冲奇异微分方程 正解 多点边值问题 MSnch不动点定理. Impulsive singular differential equations, positive solutions, multipoint boundary value problems, MSnch fixed point theorem
分类号 O175.8 [理学—基础数学]
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参考文献20

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同被引文献21

  • 1刘振斌,刘立山.Banach空间中一阶微分方程组的无穷边值问题解的存在性[J].数学学报（中文版）,2007,50(1):97-104. 被引量：8
  • 2Ma Ruyun. Existence of solutions of a nonlinear m-point boundary value problems[J]. J Math Anal Appl, 2001, 256(2): 556-567.
  • 3Zhao Yulin, Chen Haibo. Existence of multiple positive solutions for m-point boundary value problems in Banach spaces[J]. J Comput Appl Math, 2008, 215(1): 79-90.
  • 4Sun Jinxian, Xu Xian, O'Regan D. Nodal solutions for m-point boundary value problems using bifurcation methods[J]. Nonlinear Anal, 2008, 68(10): 3034-3046.
  • 5Li Yaohong, Wei Zhongli. Multiple positive solutions for nth order multi-point boundary value Problem[J]. Boundary Value Problems, 2010, ID708367, 11pages.
  • 6Su Hua, Wei Zhongli, Zhang Xiaoyan, et al. Positive solutions of n-order m-order muiti-point boundary value system[J]. Appl Math Comput, 2007, 188(2): 1234-1243.
  • 7Henderson J, Ntouyas S K. Existence of positive solutions for systems of nth-order three-point nonloeal boundary value problems[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2007, 18: 1-12.
  • 8Xu Jiafa, Yang Zhilin. Positive solutions for a systems of nth-order nonlinear boundary value problems[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2011, 4: 1-16.
  • 9Xie Shengli, Zhu Jiang. Positive solutions for the systems of nth-order singular nonlocal boundary value problems[J]. J Appl Math comput, 2011, 37(1-2): 119-132.
  • 10Leggett R W, Williams L R. Multiple positive fixed points of nonlinear operator on ordered Banach spaces[J]. Indiana Univ Math Journal, 1979, 28: 673-688.

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二级引证文献19

系统科学与数学
2011年 第7期

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