一个奇摄动四阶微分方程的非线性混合边值问题

doi:10.6040/j.issn.1671-9352.0.2014.090

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (03): 67-72.doi: 10.6040/j.issn.1671-9352.0.2014.090

一个奇摄动四阶微分方程的非线性混合边值问题

陈雯, 姚静荪, 杨雪洁

安徽师范大学数学计算机科学学院, 安徽芜湖 241003

收稿日期:2014-03-21 修回日期:2014-09-30 出版日期:2015-03-20 发布日期:2015-03-13
通讯作者: 姚静荪(1956- ), 女, 教授, 研究方向为奇异摄动.E-mail:jsyao@mail.ahnu.edu.cn E-mail:jsyao@mail.ahnu.edu.cn
作者简介:陈雯(1988- ), 女, 硕士研究生, 研究方向为奇异摄动.E-mail:maggie1002@163.com
基金资助:
国家自然科学基金资助项目(11271020)

A nonlinear mixed boundary value problem for singularly perturbed forth-order differential equation

CHEN Wen, YAO Jing-sun, YANG Xue-jie

College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China

Received:2014-03-21 Revised:2014-09-30 Online:2015-03-20 Published:2015-03-13

摘要/Abstract

摘要： 研究了一个带非线性混合边界条件的四阶非线性微分方程的奇摄动边值问题。运用合成展开法构造了该问题的形式渐近解, 并利用微分不等式理论证明了该问题解的存在性, 给出了渐近解关于精确解的误差估计。

关键词: 奇摄动, 四阶微分方程, 微分不等式理论, 合成展开法

Abstract: A singularly perturbed boundary value problem for forth-order nonlinear differential equation with nonlinear mixed boundary condition is studied. The formal asymptotic solution is constructed by using the composite expansion method. According to the theory of differential inequalities, the existence of solution for the problem is proved and the error estimate of asymptotic solution is given.

Key words: forth-order differential equation, composite expansion method, singular perturbation, the theory of differential inequality

中图分类号:

O175.14

陈雯, 姚静荪, 杨雪洁. 一个奇摄动四阶微分方程的非线性混合边值问题[J]. 山东大学学报（理学版）, 2015, 50(03): 67-72.

CHEN Wen, YAO Jing-sun, YANG Xue-jie. A nonlinear mixed boundary value problem for singularly perturbed forth-order differential equation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 67-72.

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一个奇摄动四阶微分方程的非线性混合边值问题

A nonlinear mixed boundary value problem for singularly perturbed forth-order differential equation

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