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多点边值问题的Green函数
  • ISSN号：1007-6573
  • 期刊名称：徐州师范大学学报(自然科学版)
  • 时间：0
  • 页码：6112-6117
  • 语言：中文
  • 分类：O175.08[理学—数学;理学—基础数学]
  • 作者机构：[1]北京理工大学理学院数学系,北京100081
  • 相关基金：国家自然科学基金资助项目（10671012）;教育部高校博士点专项基金资助项目（20050007011）
  • 相关项目：微分系统边值问题中的非线性分析
作者： 葛渭高|
关键词： 微分方程, 边值问题, GREEN函数, differential equation, boundary value problem, Green function
中文摘要：

Green函数是研究非线性常微分方程边值问题的重要工具.借助Green函数将微分方程边值问题解的存在性转化成算子不动点的存在性,便于给出边值问题的有解性、多解性以及唯一性的条件.本文给出半齐次线性边值问题Green函数的一般定义,它适用于二阶及高阶方程的两点和多点边值问题,并给出计算方法和若干算例.

英文摘要：

Green function is an important tool in the study of boundary value problems（BVPs） of ordinary differential equations（ODEs）.By use of Green function,a problem for the existence of solutions to BVPs of ODEs can be changed into one for the existence of fixed points to a corresponding operator,and in this way it is easier to present conditions for the solvability of a given problem.This paper presents a general definition of Green function for semi-homogeneous BVPs,which is suitable to both 2-point and multi-point BVPs of 2nd-order and higher-order equations.The method of calculation of Green function and some examples are given.Furthermore,the definition is also suitable to the case where the boundary condition is given in the form of linear integration.

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微分系统边值问题中的非线性分析
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