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Symmetric Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem 被引量：3

Symmetric Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem
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摘要 In this paper, we consider the following second order three-point boundary value problem u″（t）＋a（t）f（u（t））=0,0〈t〈1,u（0）-u（1）=0,u＇（0）-u＇（1）=u（1/2）,where a ： （0, 1） → [0, ∞） is symmetric on （0, 1） and may be singular at t = 0 and t = 1, f ： [0, ∞） → [O, ∞） is continuous. By using Krasnoselskii＇s fixed point theorem ia a cone, we get some existence results of positive solutions for the problem. The associated Green＇s function for the three-point boundary value problem is also given. In this paper, we consider the following second order three-point boundary value problem u″（t）＋a（t）f（u（t））=0,0〈t〈1,u（0）-u（1）=0,u＇（0）-u＇（1）=u（1/2）,where a ： （0, 1） → [0, ∞） is symmetric on （0, 1） and may be singular at t = 0 and t = 1, f ： [0, ∞） → [O, ∞） is continuous. By using Krasnoselskii＇s fixed point theorem ia a cone, we get some existence results of positive solutions for the problem. The associated Green＇s function for the three-point boundary value problem is also given.
作者 Yong-ping Sun
机构地区 Department of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2006年第1期65-74,共10页 应用数学学报（英文版）
基金 Supported by the National Natural Science Foundation of China(No.10471075) National Natural Science Foundation of Shandong Province of China(No.Y2003A01) Foundation of Education Department of Zhejiang Province of China(No.20040495,No.20051897)
关键词 Symmetric positive solution three-point boundary value problem fixed point theorem EXISTENCE Symmetric positive solution, three-point boundary value problem, fixed point theorem, existence
分类号 O175.8 [理学—基础数学]
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参考文献18

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同被引文献14

  • 1李淑红,张马彪.一类二阶三点边值问题正解的存在性[J].丽水学院学报,2004,26(5):1-5. 被引量：7
  • 2彭世国,朱思铭.泛函微分方程周期边值问题的正解[J].数学年刊（A辑）,2005,26(3):419-426. 被引量：9
  • 3PengShiguo.POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL SYSTEMS[J].Annals of Differential Equations,2005,21(2):192-197. 被引量：1
  • 4Li Shuhong Sun Yongping Department of Mathematics, Lishui University, Lishui 323000,China,Department of Applied Mathematics, Zhejiang Sci-Tec University, Hangzhou 310018, China,Department of Electron and Information, Zhejiang University of Media and Communications, Hangzhou 310018, China..NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM[J].Applied Mathematics(A Journal of Chinese Universities),2007,22(1):37-47. 被引量：2
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  • 6[2]Il'in V A,Moiseev E I.Nonlocal boundary value problem of the second kind for a Sturm-Liouvill operator[J].Differential Equations,1987,23(8):979-987.
  • 7[3]Gupta C P.Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations[J].J.Math.Anal.Appl.,1992,168:540-551.
  • 8[4]Du Zeng-ji,Xue Chun-yan,Ge Wei-gao.Multiple solutions for three-point boundary value problem with nonlinear terms depending on the firrst order derivative[J].Archiv der Mathematik,2005,84:341-349.
  • 9[5]Yang Chen,Zhai Cheng-bo,Yan Ju-rang.Positive solutions of the three-point boundary value proplem for second order differential equations with an advanced argument[J].Nonl.Anal.2006,65:2013-2023.
  • 10[6]Bai Chuan-zhi,Xu Xin-ya.Positive solutions for a functional delay second-order three-point boundary value problem[J].Electron.J.Differential Equations,2006,41:1-11.

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Acta Mathematicae Applicatae Sinica
2006年 第1期

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