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| 三阶两点边值问题单调递减正解的存在惟一性 | |
| 引用本文： | 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].山东大学学报(理学版),2008,43(12):84-87. |
| 作者姓名： | 续晓欣 梁月亮 桑彦彬 |
| 作者单位： | 1. 中北大学理学院数学系,山西,太原,030051 2. 中北大学理学院数学系,山西,太原,030051;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 |
| 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 |
| 收稿时间： | 2008-09-21 |
The existence and uniqueness of a monotone decreasing positive solution of a third-order two-point boundary value problem |
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| XU Xiao-xin,HANG 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].Journal of Shandong University,2008,43(12):84-87. | |
| Authors: | XU Xiao-xin HANG Yue-liang SANG Yan-bin |
| Institution: | 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 |
| 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。 |
| Keywords: | boundary value problem fixed-point theorem monotone decreasing positive solution |
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