二阶时滞微分方程边值问题的上下解方法

王宏洲, Richard M. TIMONEY

数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 489-494.

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PDF(379 KB)
数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 489-494. DOI: 10.12386/A2010sxxb0054
论文

二阶时滞微分方程边值问题的上下解方法

    王宏洲1, Richard M. TIMONEY2
作者信息 +

Upper and Lower Solutions Method for Second Order Boundary Value Problems with Delay

    Hong Zhou WANG1, Richard M. TIMONEY2
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文章历史 +

摘要

主要利用上下解方法和Schauder不动点定理,研究一类二阶时滞微分方程边值 问题的正解存在性.为了验证结论的正确性, 本文在结尾部分给出了两个例子.

 

Abstract

We consider the existence of positive solutions for a class of second order boundary value problems with delay. By using upper and lower solutions method and Schauder fixed point theorem, we obtain some existence results of positive solutions. The results are illustrated with some examples.

 

关键词

边值问题 / 时滞 / 上下解

Key words

boundary value problem / delay / upper and lower solutions

引用本文

导出引用
王宏洲, Richard M. TIMONEY. 二阶时滞微分方程边值问题的上下解方法. 数学学报, 2010, 53(3): 489-494 https://doi.org/10.12386/A2010sxxb0054
Hong Zhou WANG, Richard M. TIMONEY. Upper and Lower Solutions Method for Second Order Boundary Value Problems with Delay. Acta Mathematica Sinica, Chinese Series, 2010, 53(3): 489-494 https://doi.org/10.12386/A2010sxxb0054

参考文献


[1] Tadeusz J., Solvability of three point boundary value problems for second order differential equations with deviating arguments, Journal of Mathematical Analysis and Applications, 2005, 312: 620--636.

[2] Tadeusz J., Functional differential equations of second order, Bulletin of the Belgian Mathematical Society, 2003, 10: 291--298.

[3] Jiang D. Q., Zhang L. L., Positive solutions for boundary value problems of second-order delay differential equations, Acta Mathematica Sinica, Chinese Series, 2003, 46(4): 739--746.

[4] Shu X. B., Xu Y. T., Triple positive solutions for a class of boundary value problems of second-order functional differential equations, Acta Mathematica Sinica, Chinese Series, 2005, 48(6): 1113--1120.

[5] Shu X. B., Huang L. H., Li Y. J., Triple positive solutions for a class of boundary value problems for second-order neutral functional differential equations, Nonlinear Analysis, 2006, 65(4): 825--840.

[6] Ma D. X., Ge W. G., Existence and iteration of solutions for a multi-point boundary value problem with a p-Laplacian operator, Acta Mathematica Sinica, Chinese Series, 2008, 51(3): 447--456.

基金

国家自然科学基金资助项目(10671012)

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