二阶三点边值问题解的存在性与唯一性  

Existence and Uniqueness of Solutions of Second-order Three-point Boundary Value Problems

作　　者：朱卫明[1] 刘锡平[1] 贾梅[1] 张鲁潮[1] 孙凤文[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《数学的实践与认识》2008年第18期179-186,共8页Mathematics in Practice and Theory

基　　金：上海市教委科研基金(05EZ52)

摘　　要：利用单调迭代方法,研究了反序上、下解条件下的二阶微分方程三点边值问题解的存在性与唯一性,分别得到解存在与唯一的充分条件,在满足解的唯一性的条件下,给出了求解的迭代序列及误差估计式.This paper studies the existence and uniqueness of solutions of second-order threepolnt boundary value problems with lower and upper solutions in the reversed order, obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method, and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution.

关 键 词：边值问题 单调迭代方法 反序上下解 存在性与唯一性 误差估计 

分 类 号：O175.8[理学—数学] O175.15[理学—基础数学]