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二阶三点边值问题正解的存在性 被引量：5

Existence of positive solutions for a second-order three-point boundary value problem
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摘要 利用不动点指数定理研究了一类二阶非线性常微分方程的三点边值问题正解的存在性问题,得到了至少存在一个或无穷多个正解的几个充分条件. In this paper, the existence of multiple positive solutions for a second-order threepoint boundary value problem is investigated. By using the fixed point index theorem, several sufficient conditions for the existence of at least one or infinte positive solutions are obtained.
作者 李淑红
机构地区 丽水学院成教学院
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2007年第4期441-446,共6页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 浙江省高校重点学科资金(2005) 浙江省自然科学基金(Y605144)
关键词 三点边值问题 不动点指数 正解 存在性 three-point boundary value problem fixed point index positive solution existence
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献14

  • 1Il'in V A, Moiseev E I. Nonlocal boundary value problem of the second kind for a Sturm-Liouvill operator in its differential and finite difference aspects[J]. Differential Equations, 1987, 23(7): 803-810.
  • 2Il'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.
  • 3Gupta 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.
  • 4Gupta C P, Trofimchuk S I. A sharper condition for the solvability of a three-point second order boundary value problem[J]. J Math Anal Appl, 1997,205: 586-597.
  • 5Ma R.Positive solutions of a nonlinear three-point boundary value problem[J]. Electron J Differential Equations, 1999, 34: 1-8.
  • 6Gupta C P. Solvability of an m-point nonlinear boundary value problem for second order ordinary differential equations[J]. J Math Anal Appl, 1995,189: 575-584.
  • 7Ma R. Existence theorems for a second order three-point boundary value problem[J].J Math Anal Appl,1997,212: 430-442.
  • 8Liu B. Positive solutions of a nonlinear three-point boundary value problem[J].Appl Math Comput, 2002, 132: 11-28.
  • 9Sun Y,Liu L. Solvability for a nonlinear second-order three-point boundary value problem[J].J Math Anal Appl, 2004, 296: 265-275.
  • 10Infante G,Eigenvalues of some non-local boundary value problems[J]. Proc Edinburgh Math Soc, 2003, 46: 75-86.

二级参考文献24

  • 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[1]Il'in V A, Moiseev EI. Nonlocal boundary value problem of the sevond kind for a Sturm-Liouvill operator in its differential and finite difference aspects[J] Differential Equations, 1987,23(7):803～810
  • 3[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
  • 4[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
  • 5[4]Ma R. Positive solutions of a nonlinera three-point boundary value problems[J]. Electron J Differential Equations, 1999,34:1～8
  • 6[6]Infante G. Eigenvalues of some non-local boundary value problems[J]. Proc Eidinburgh Math Soc,2003,46:75～86
  • 7[7]Guo D, Lakshmikantham V. Nonlinear Problems in Abstract Cones[M].Orlando:Academic Press, 1988.94～95
  • 8[8]郭大钩.非线性泛函分析[M].济南:山东科技出版社,1985.310～311
  • 9[9]Ma R.Existence theorems for a second order three-point boundary value problem[J].J Math Anal Appl, 1997,212:430～442
  • 10[10]Gupta C P, Trofimchuk SI. A sharper condition for the solvability of a three-point second order boundary value problem[J]. J Math Anal Appl, 1997,205:586～597

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引证文献5

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高校应用数学学报（A辑）
2007年 第4期

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