奇异非自治三阶两点边值问题的正解存在性

J4 ›› 2012, Vol. 47 ›› Issue (6): 10-15.

奇异非自治三阶两点边值问题的正解存在性

姚庆六

南京财经大学应用数学系, 江苏南京 210003

收稿日期:2011-03-17 出版日期:2012-06-20 发布日期:2012-06-26
作者简介:姚庆六(1946- ), 男, 教授, 研究方向为非线性常微分方程. Email: yaoqingliu2002@hotmail.com
基金资助:
国家自然科学基金资助项目 (11071109)

Existence of a positive solution of singular nonautonomous third-order two-point boundary value problems

YAO Qing-liu

Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, Jiangsu, China

Received:2011-03-17 Online:2012-06-20 Published:2012-06-26

摘要/Abstract

摘要：

研究一类非自治非线性三阶两点边值问题的正解, 其中允许非线性项关于时间变元和空间变元为奇异的。通过构造适当的控制函数并且利用锥上的 Guo-Krasnosel’skii 不动点定理建立了一个正解存在定理。

关键词: 奇异常微分方程; 非自治边值问题; 正解; 存在性

Abstract:

The positive solution of a class of nonautonomous nonlinear third-order two-point boundary value problems is studied, where the nonlinear term is allowed to be singular with respect to the time and space variables. By constructing suitable dominated functions and applying Guo-Krasnosel’skii fixed point theorem on a cone, an existence theorem of a positive solution is established.

Key words: singular ordinary differential equation; nonautonomous boundary value problem; positive solution; existence

姚庆六. 奇异非自治三阶两点边值问题的正解存在性[J]. J4, 2012, 47(6): 10-15.

YAO Qing-liu. Existence of a positive solution of singular nonautonomous third-order two-point boundary value problems[J]. J4, 2012, 47(6): 10-15.

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