二阶三点边值问题两个正解的存在性

续晓欣; 梁月亮

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二阶三点边值问题两个正解的存在性

应用基础研究 | 更新时间：2026-09-14

- 二阶三点边值问题两个正解的存在性
- Existence of Double Positive Solutions of Two-order Three-point Boundary Value Problem
- 中北大学学报（自然科学版） 2009年30卷第2期页码：105-109
- 作者机构：
  
  中北大学理学院
- 作者简介：
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- 纸质出版：2009
- 稿件说明：
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续晓欣, 梁月亮. 二阶三点边值问题两个正解的存在性[J]. 中北大学学报（自然科学版）, 2009,30(2):105-109.

续晓欣, 梁月亮. Existence of Double Positive Solutions of Two-order Three-point Boundary Value Problem[J]. 2009, 30(2): 105-109.
续晓欣, 梁月亮. 二阶三点边值问题两个正解的存在性[J]. 中北大学学报（自然科学版）, 2009,30(2):105-109. DOI：

续晓欣, 梁月亮. Existence of Double Positive Solutions of Two-order Three-point Boundary Value Problem[J]. 2009, 30(2): 105-109. DOI：

摘要

利用Guo-Krasnoseskill’s锥拉伸与锥压缩型不动点定理及格林函数的性质

研究了非线性二阶三点边值问题

获得了其正解存在性的新结果.在此基础上

给出了此边值问题两个正解存在性的几个充分条件

推广和改进了以前文献的相关结果

因此本文在边值问题的进一步研究方面具有一定的理论意义.

Abstract

A class of nonlinear two-order three-point boundary value problem is considered

and the existence of positive solutions is obtained by making use of the Guo-Krasnoseskill's fixed point theorem of cone expansion-compression type and the properties of the Green function.On the basis of that

several sufficient conditions of the existence of double positive solutions are deduced for the nonlinear two-order three-point boundary value problem.The results have generalized and improved the related ones of the known references

which has theoretical significance on problem boundary value.

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references

Han X.Positive solutions for a three-point boundary value problem at resonance[J].J.Math.Anal.Appl.,2007,336:556-568.

Liu B,Liu L,Wu Y.Positive solutions for a singular second-order three-point boundary value problem[J].Appl.,Math.Comput,2008,196:532-541.

Liu Z,Li F.Multiple positive solutions of nonlinear two-point boundary value problems[J].J.Math.Anal.Appl.1996,203:610-625.

Liang R,Peng J,Shen J.Positive solutions to a generalized second order three-point boundary value problem[J].A.Math.Comput,2008,196:931-940.

Luo H,Ma Q.Positive solutions to a generalized second-order three point boundary value problem on time scales[J].Electron J.Differ.Equat,2005,1:1-14.

Guo D.Lakshmikantham V.Nonlinear Problems in Abstract Cones[M].San Diego:Academic Press,1988.

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