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二阶三点边值问题解的存在性与唯一性
引用本文:朱卫明,刘锡平,贾梅,张鲁潮,孙凤文.二阶三点边值问题解的存在性与唯一性[J].数学的实践与认识,2008,38(18).
作者姓名:朱卫明  刘锡平  贾梅  张鲁潮  孙凤文
作者单位:上海理工大学,理学院,上海,200093
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.

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

Existence and Uniqueness of Solutions of Second-order Three-point Boundary Value Problems
ZHU Wei-ming,LIU Xi-ping,JIA Mei,ZHANG Lu-chao,SUN Feng-wen.Existence and Uniqueness of Solutions of Second-order Three-point Boundary Value Problems[J].Mathematics in Practice and Theory,2008,38(18).
Authors:ZHU Wei-ming  LIU Xi-ping  JIA Mei  ZHANG Lu-chao  SUN Feng-wen
Abstract:This paper studies the existence and uniqueness of solutions of second-order three-point 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.
Keywords:boundary value problem  monotone iterative method  upper and lower solutions in reversed order  existence and uniqueness  error estimate
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