Positive Solutions to a Second-Order Singular Periodic Boundary Value Problem with Derivative Argument

赵东霞; 王宏洲

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Positive Solutions to a Second-Order Singular Periodic Boundary Value Problem with Derivative Argument

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- Positive Solutions to a Second-Order Singular Periodic Boundary Value Problem with Derivative Argument
- 含导数项的奇异二阶周期边值问题的正解
- Issue 4, Pages: 291-296(2008)
- 作者机构：
  
  1. 中北大学理学院
  2. 北京理工大学理学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2008
- 稿件说明：
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赵东霞, 王宏洲. Positive Solutions to a Second-Order Singular Periodic Boundary Value Problem with Derivative Argument[J]. 2008, (4): 291-296.
DOI：

赵东霞, 王宏洲. Positive Solutions to a Second-Order Singular Periodic Boundary Value Problem with Derivative Argument[J]. 2008, (4): 291-296. DOI：

摘要

在二阶非线性微分方程周期边值问题的基础上

利用锥映射不动点定理

讨论了带有导数项的二阶非线性周期边值问题的正解的存在性

并且允许非线性项具有奇异性这一限制条件

最后给出了解的存在性定理

还把这一结果应用于一个具体的二阶边值问题中

同时对前人的结果进行了改进和推广.

Abstract

On the basis of nonlinear second-order periodic boundary value problem

the paper mainly discusses the existence of positive solutions to a class of nonlinear second-order singular periodic boundary value problem with derivative argument by using Krasnoselskii fixed point theorem of cone map.The sufficient conditions for positive periodic solutions are obtained.The results are applied to a detailed example

and the traditional results are improved.

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references

Jiang Daqing.On the existence of positive solutions to second-order periodic BVPs[J].Mathematica Acta Scientia,1998,18(Supp):31-35.

万阿英,蒋达清.奇异超线性二阶周期边值问题的正解[J].吉林大学(自然科学学报),2001(2):25-27.Wan Aying,Jiang Daqing.Positive solutions to a singular superlinear second order periodic boundary value problem[J].ACTA Scientiarum Naturalium Universitatis Jilinensis,2001(2):25-27.(in Chinese)

李永祥.二阶非线性常微分方程的正周期解[J].数学学报,2002(3):481-488.Li Yongxiang.Positive periodic solutions of nonlinear second order ordinary differential equations[J].ACTAMathematicasinica,2002(3):481-488.(in Chinese)

Wang Junyu,Jiang Daqing.A singular nonlinear second order boundary value problem[J].Tohuko Math J,1998,143:60-95.

Ding Wei,Han Maoan,Yan Jurang.Periodic boundary value problems for the second order functional differentialequations[J].J.Math.Anal.Appl.2004,298:341-351.

Torres P J.Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskiifixed point theorem[J].J.Diff.Equs,2003,190:643-662.

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