一类半无穷区间上三点边值问题无界解的存在性

数学物理学报 ›› 2012, Vol. 32 ›› Issue (3): 489-499.

一类半无穷区间上三点边值问题无界解的存在性

廉海荣¹|崔子嘉²|张帅³

1.中国地质大学(北京)数理学院北京 100083|2.北京师范大学天文系北京 100875|3.中国地质大学(北京)科学研究院北京 100083

收稿日期:2010-12-01 修回日期:2012-03-06 出版日期:2012-06-25 发布日期:2012-06-25
基金资助:
中央高校基本科研业务费专项资金(2011YYL077, 2011YXL044)和国家自然科学基金(11101385)资助

The Existence of Unbounded Solutions to Three-point Boundary Value Problem over a Semi-infinite Interval

LIAN Hai-Rong¹, CUI Zi-Jia², ZHANG Shuai³

1.School of Sciences, China University of Geoscience, Beijing 100083|2.Department of Astronomy, Beijing Normal University, Beijing 100875|3.Institute of Earth Sciences, China University of Geoscience, Beijing 100083

Received:2010-12-01 Revised:2012-03-06 Online:2012-06-25 Published:2012-06-25
Supported by:
中央高校基本科研业务费专项资金(2011YYL077, 2011YXL044)和国家自然科学基金(11101385)资助

摘要/Abstract

摘要：

讨论了一类半无穷区间上二阶非线性常微分方程三点边值问题的可解性. 通过建立无界上下解理论, 利用上下解, Schäuder不动点定理和不等式技巧, 给出了这类问题解存在的充分条件. 该文的创新之一就是建立了多点边值问题的无界上下解理论.

关键词: 三点边值问题, 无穷区间, 上下解, 不动点定理, Nagumo 条件

Abstract:

This paper discusses the existence of unbounded solutions to three-point boundary value problems of second order nonlinear differential equations on the half line. By establishing the unbounded upper and lower solutions theory, using the upper and lower solutions, the Schäuder fixed point theorem and inequality technique, sufficient conditions are obtained to guarantee the existence of solution. One interesting point is that the unbounded upper and lower solutions theory is established for three-point boundary value problem.

Key words: Three-point boundary value problem, Infinite interval, Upper and lower solution, Fixed point theory, Nagumo condition

中图分类号:

34B10

廉海荣, 崔子嘉, 张帅. 一类半无穷区间上三点边值问题无界解的存在性[J]. 数学物理学报, 2012, 32(3): 489-499.

LIAN Hai-Rong, CUI Zi-Jia, ZHANG Shuai. The Existence of Unbounded Solutions to Three-point Boundary Value Problem over a Semi-infinite Interval[J]. Acta mathematica scientia,Series A, 2012, 32(3): 489-499.

参考文献

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