Monotone iterative method for the second-order three-point boundary value problem with upper and lower solutions in the reversed order

被引：17

作者：

Li, Fangfei ^{[1
]}

Sun, Jitao ^{[1
]}

Jia, Mei ^{[2
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Shanghai Univ Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 09期

关键词：

Upper and lower solutions; Reversed order; Monotone and iterative method; Second-order three point boundary value problem; EXISTENCE; EQUATIONS; UNIQUENESS;

D O I：

10.1016/j.amc.2010.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order. The sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method, meantime, the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given. Some results of previous literature are extended and improved. A numerical example is also included to illustrate the effectiveness of the proposed results. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：4840 / 4847

页数：8

共 50 条

[1] Existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order
Li, Fangfei
Jia, Mei
Liu, Xiping
Li, Chuling
Li, Gaoshang
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (08) : 2381 - 2388
[2] UPPER AND LOWER SOLUTIONS FOR A SECOND-ORDER THREE-POINT SINGULAR BOUNDARY-VALUE PROBLEM
Zhang, Qiumei
Jiang, Daqing
Weng, Shiyou
Gao, Haiyin
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2009,
[3] Upper and lower solutions method and a second order three-point singular boundary value problem
Zhang, Qiumei
Jiang, Daqing
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (04) : 1059 - 1070
[4] Positive Solutions of a Second-Order Three-point Boundary Value Problem
李兆兴
张中新
[J]. Communications in Mathematical Research, 2002, (02) : 130 - 136
[5] Positive solutions for a second-order three-point discrete boundary value problem
Du Z.
[J]. Journal of Applied Mathematics and Computing, 2008, 26 (1-2) : 219 - 231
[6] Positive solutions for a singular second-order three-point boundary value problem
Liu, Bingmei
Liu, Lishan
Wu, Yonghong
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 196 (02) : 532 - 541
[7] Multiple positive solutions for a second-order three-point boundary value problem
Li, Jianli
Shen, Jianhua
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (01) : 258 - 268
[8] Existence of at least three solutions of a second-order three-point boundary value problem
Khan, RA
Webb, JRL
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (06) : 1356 - 1366
[9] A second-order singular three-point boundary value problem
Singh, P
[J]. APPLIED MATHEMATICS LETTERS, 2004, 17 (08) : 969 - 976
[10] MONOTONE METHOD FOR SECOND ORDER THREE-POINT BOUNDARY VALUE PROBLEMS
Li Longtu
Tan Lifang (Department of Applied Mathematics and Applied Software
[J]. Journal of Central South University, 1995, (01) : 76 - 78

← 1 2 3 4 5 →