数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 718-729.

• 论文 • 上一篇    下一篇

一类二阶常微分方程m点边值问题的解法

李兴昌|赵增勤   

  1. 曲阜师范大学数学科学学院 山东曲阜 273165
  • 收稿日期:2008-09-08 修回日期:2009-11-29 出版日期:2010-05-25 发布日期:2010-05-25
  • 基金资助:

    国家自然科学基金 (10871116)、山东省自然科学基金(Y2006A04)和高教博士点专项科研基金(200804460001) 资助

Solutions of Some m-point Boundary Value Problems for Second-order Differential Equations

 LI Xing-Chang, ZHAO Zeng-Qin   

  1. School of Mathematical Sciences, Qufu Normal University, Shandong Qufu |273165
  • Received:2008-09-08 Revised:2009-11-29 Online:2010-05-25 Published:2010-05-25
  • Supported by:

    国家自然科学基金 (10871116)、山东省自然科学基金(Y2006A04)和高教博士点专项科研基金(200804460001) 资助

摘要:

该文研究一类二阶常微分方程, 给出了所述线性方程在几种m点边界条件下解的存在惟一性及其解的解析表达式, 作为应用的例子, 作者对一类非线性边值问题给出了正解的迭代求法.

关键词: 二阶微分方程, m 点边值问题, 解析表达式, 迭代求解

Abstract:

In this paper, we consider some m-point boundary value problems of second-order differential equations. We give the uniqueness and the  exact expressions of the solutions for the linear differential equations with some m-point boundary conditions. As applications, we study the solution by iteration method for some nonlinear singular boundary value problems.

Key words: Second-order differential equation, m-point boundary value problem, Analytic expression, Solution by iteration method

中图分类号: 

  • 34A05