三阶两点边值问题单调递减正解的存在惟一性

J4 ›› 2008, Vol. 43 ›› Issue (12): 84-87.

三阶两点边值问题单调递减正解的存在惟一性

续晓欣¹,梁月亮^{1, 2},桑彦彬³

1. 中北大学理学院数学系, 山西太原 030051; 2. 同济大学应用数学系, 上海 200092;
3. 山东大学数学学院, 山东济南 250100

收稿日期:2008-09-21 出版日期:2008-12-16 发布日期:2009-11-09
通讯作者: 梁月亮 shaguamoon@126.com

The existence and uniqueness of a monotone decreasing positive solution of a third-order two-point boundary value problem

XU Xiao-Xin¹, LIANG Yue-Liang^{1, 2}, SANG Yan-Bin³

1. Department of Mathematics,North University of China, Taiyuan 030051, Shanxi, China;
2. Department of Applied Mathematics,Tongji University, Shanghai 200092, China;
3. School of Mathematics and System Sciences,Shandong University, Jinan 250100, Shandong, China

Received:2008-09-21 Online:2008-12-16 Published:2009-11-09

摘要/Abstract

摘要：

利用巴拿赫不动点定理和积分算子来研究非线性三阶两点边值问题:u″+q(u′)f(t,u)=0, a.e. t∈［0,1］,u′(0)=A, u(1)=B, u″(0)=C。其中 A≤0,B≥0,C≤0为常数,在此基础上给出了此边值问题单调递减非平凡正解的存在惟一性的充分条件。

关键词: 边界值问题;不动点定理;单调递减正解

Abstract:

By using Banach fixed point theorem in cone, one sufficient condition of the existence and uniqueness of a monotone decreasing positive solution was established to the nonlinear third-order two-point boundary value problem:u″+q(u′)f(t,u)=0, a.e. t∈［0,1］,u′(0)=A, u(1)=B, u″(0)=C,　where A≤0,　B≥0,　C≤0　were constants。

Key words: boundary value problem; fixedpoint theorem; monotone decreasing positive solution

中图分类号:

O175.8

续晓欣梁月亮桑彦彬. 三阶两点边值问题单调递减正解的存在惟一性[J]. J4, 2008, 43(12): 84-87.

XU Xiao-Xin, LIANG Yue-Liang, SANG Yan-Bin. The existence and uniqueness of a monotone decreasing positive solution of a third-order two-point boundary value problem[J]. J4, 2008, 43(12): 84-87.

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