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具有变号非线性项的奇异二阶三点边值问题的三个非零正解 被引量：4

Three Nontrival Positive Solutions for Second Order Three Point Boundary Value Problems with Sign Changing Nonlinearities
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摘要 该文研究一类具有变号非线性项的奇异二阶三点边值问题多个正解的存在性.运用Leggett-williams不动点定理在f满足一定的增长条件下,获得了至少三个非零正解存在的结果. In this paper, the existence of multiple nontrival positive solutions for a class of singular second order three point boundary value problems with sign changing nonlinearities is investigated. Growth conditions are imposed on f, which yield the existence of at least three nontrival positive solutions by using the Leggett-Williams fixed point theorem.
作者 李成 刘立山
机构地区 曲阜师范大学数学科学学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2008年第3期515-522,共8页 Acta Mathematica Scientia
基金 国家自然科学基金(10771117，10471075) 高等学校博士点专项基金(20060446001) 山东省自然科学基金(Y2007A23)资助
关键词 三点边值问题 奇异 变号 三个正解 Three point boundary value problem Singular Change of sign Three nontrival positive solutions.
分类号 O175.8 [理学—基础数学] O175.15 [理学—基础数学]
  • 相关文献

参考文献14

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二级参考文献14

  • 1Il'in V A, Moiseev E I. Nonlocal Boundary Value Problem of the Second Kind for a Sturm-Liouville Perator. Differential Equations, 1987, 23(8): 979-987
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  • 9Ma Ruyun. Positive Solutions for Second order Three-point Boundary Value Problems. Applied Mathematics Letters, 2001, 14:1-5
  • 10Ma Ruyun. Positive Solutions of a Nonlinear Three-point Boundary Value Problem. Electronic Journal of Differential Equations, 1999, 34:1-8

共引文献50

同被引文献27

  • 1郭彦平,葛渭高,董士杰.具有变号非线性项的二阶三点边值问题的两个正解[J].应用数学学报,2004,27(3):522-529. 被引量：27
  • 2GUO DAJUN,LAKSHMIKANTHAN V.Nonlinear problems in abstract cones[M].New York:Academic Press,1988.
  • 3Zhao Zengqin. Solutions and Green' s functions for some linear second-order three-point boundaryvalue problems [ J ]. Computers and Mathematics with Applications,2008, 56 : 104-113.
  • 4Du Xinsheng, Zhao Zengqin. A necessary and sufficient condition for the existence of positive solutions to singular sublinear three- point boundary value problems[ J]. Applied Mathematics and Computation2007, 186:404-413.
  • 5Du Xinsheng, Zhao Zengqin. Existence and uniqueness of positive solutions to a class of singular m-point boundary value problems [ J ]. Applied Mathematics and Computation,2008:487-493.
  • 6Gallaxdo J M. Second order differential operators with integral boundary conditions and generation of semigroups. Rocky Mountain J Math, 2000, 30:1265-1292.
  • 7Lomtatidze A, Malaguti L. On a nonlocal boundary-value problems for second order nonlinear singular differential equations. Georg Math J, 2000, 7:133-154.
  • 8Zhang X, Feng M, Ge W. Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces. Nonlinear Anal, 2008, 69:3310-3321.
  • 9Zhang G, Sun J. Positive solutions of m-point boundary value problems. J Math Anal Appl, 2004, 291: 406-418.
  • 10Zhang X, Liu L. Positive solutions of fourth-order multi-point boundary value problems with bending term. Appl Math Comput, 2007,194:321-332.

引证文献4

数学物理学报（A辑）
2008年 第3期

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