| 一类四阶常微分方程两点边值问题解的存在唯一性 |
| |
| 引用本文： | 张剑虎,刘文斌,蹇玲玲.一类四阶常微分方程两点边值问题解的存在唯一性[J].大学数学,2009,25(3). |
| |
| 作者姓名： | 张剑虎 刘文斌 蹇玲玲 |
| |
| 作者单位： | 1. 南开大学,经济研究所,天津,300071
2. 中国矿业大学,理学院,徐州,221008 |
| |
| 基金项目： | 教育部新世纪人才支持计划项目 |
| |
| 摘 要： | 利用压缩映射原理讨论了边值问题y(4)(t)=f(t,y,y′,y,″y′″),y(a)=y(b)=0,y″(a)=y″(b)=0解的存在唯一性问题,得出了当f满足Lipschitz条件时边值问题解的存在唯一性定理,并证明了当f为半线性f(t,y)时结论是最优的.同时给出了一个改进的Picard迭代误差公式,此公式保证了端点处误差为零.
|
| 关 键 词： | 存在性 唯一性 边值问题 Green函数 压缩映射原理 |
Existence and Uniqueness of Solutions of Fourth-order Boundary Value Problems for Differential Equation |
| |
| ZHANG Jian-hu,LIU Wen-bin,JIAN Ling-ling.Existence and Uniqueness of Solutions of Fourth-order Boundary Value Problems for Differential Equation[J].College Mathematics,2009,25(3). |
| |
| Authors: | ZHANG Jian-hu LIU Wen-bin JIAN Ling-ling |
| |
| Institution: | 1.Nankai Institute of Economics;Tianjin 300071;China;2.Department of Mathematics;China University of Mining and Technology;Xuzhou 221008;China |
| |
| Abstract: | Used contraction mappings fixed point theorem,this paper discussed the existence and uniqueness of boundary value problems as followes:y(4)(t)=f(t,y,y′,y″,y′″),y(a)=y(b)=0,y″(a)=y″(b)=0.We get the existence and uniqueness theorem of BVP when f satisfy Lipschitz condition,and proved that the result was the best when f was semilinear.At the same time we get an improved Picard iteration error formula which ensured the error was zero at two points. |
| |
| Keywords: | existence uniqueness boundary value problem Green function contraction mappings fixed point theorem |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
