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非线性三阶三点边值问题正解的存在性 被引量：13

Existence of positive solution for a nonlinear third-order three-point boundary value problem
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摘要 讨论非线性三阶三点边值问题u''(t)+a(t)f(u(t))=0,t∈[0,1],u(0)=u′(0)=0,u(1)=αu′(η).在给出相应的Green函数并讨论其性质的基础上,运用Guo-Krasnoselskii不动点定理获得了上述三阶三点边值问题正解的存在性. This paper is concerned with the following nonlinear third-order three-point boundary value problem {u＇＇（t）＋a（t）f（u（t））=0,t∈,u（0）=u′（0）=0,u（1）=αu′（η）.The corresponding Green＇s function is given and its properties are discussed.And then,the existence of positive solution for the above boundary value problem is obtained by using the Guo-Krasnoselskii fixed point theorem.
作者 孙建平 张小丽
机构地区 兰州理工大学理学院
出处 《西北师范大学学报（自然科学版）》 CAS 北大核心 2012年第3期1-4,31,共5页 Journal of Northwest Normal University(Natural Science)
基金 国家自然科学基金资助项目(10801068)
关键词 三阶三点边值问题 GREEN函数 正解 存在性 不动点 third-order three-point boundary value problem Green＇s function positive solution existence fixed point
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献7

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二级参考文献9

  • 1CHEN H B. Positive solutions for the nonhomogeneous three-point boundary value problem of second-order differential equations [J].Mathematical and Computer Modelling, 2007, 45:844-852.
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共引文献3

同被引文献65

  • 1姚庆六.一类复合型奇异三阶三点边值问题正解的存在性[J].浙江大学学报（理学版）,2012,39(4):381-384. 被引量：1
  • 2曹珂,赵慧霞.非线性奇异三阶三点边值问题单调正解的存在性[J].甘肃联合大学学报（自然科学版）,2011,25(5):13-16. 被引量：1
  • 3沈建和,余赞平,周哲彦.非线性三阶常微分方程的非线性三点边值问题解的存在性[J].纯粹数学与应用数学,2007,23(3):355-360. 被引量：14
  • 4Graef J R,Yang B.Multiple positive solutions to a three point third order boundary value problem[J].Discrete Contin.Dyn.Syst,2005(S1):1-8.
  • 5Guo L,Sun J,Zhao Y.Existence of positive solution for nonlinear third-order three point boundary value problem[J].Nonlinear Anal,2007(14):93-111.
  • 6Boucherif A,Al-Malki N.Nonlinear three-point third order boundary value problems[J].Appl.Math.Comput,2007(190):1168-1177.
  • 7Sun Y.Positive solutions of singular third order three point boundary value problems[J].J.Math.Anal.Appl,2005(306):589-603.
  • 8Yu H,Lu H,Liu Y.Multiple positive solutions to third-order three-point singular semi positive boundary value problem[J].Proc.Indian Acad.Sci.Math.Sci,2004(114):409-422.
  • 9Guo L J,Sun J P,Zhao Y H.Existence of positive solutions for nonlinear third-order three-point boundary value problems[J].Nonlinear Anal,2008(68):3151-3158.
  • 10Graef J R,Webb J R.Third order boundary value problems with nonlocal boundary conditions[J].Nonlinear Anal,2009(71):1542-1551.

引证文献13

二级引证文献25

西北师范大学学报（自然科学版）
2012年 第3期

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