UNIQUE EXISTENCE RESULTS AND NUMERICAL SOLUTIONS FOR FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

被引：0

作者：

Wang, Hui ^{[1
]}

Zhang, Lingling ^{[1
,2
]}

Wang, Xiaoqiang ^{[3
]}

机构：

[1] Taiyuan Univ Technol, Coll Math, Yingze West Rd, Taiyuan 030024, Shanxi, Peoples R China

[2] Beijing Inst Technol, State Key Lab Explos Sci & Technol, Zhongguancun South St, Beijing, Peoples R China

[3] Florida State Univ, Dept Sci Comp, Tallahassee, FL 32306 USA

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2019年 / 9卷 / 05期

关键词：

Existence and uniqueness; positive solution; impulsive differential equations; fixed point theorem for sum operator; numerical solution; ELASTIC BEAM EQUATION; MULTIPLE POSITIVE SOLUTIONS; OPERATORS; SYSTEM;

D O I：

10.11948/20180158

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The work is concerned with three kinds of fourth-order impulsive differential equations with nonlinear boundary conditions. We at first focused on studying the existence and uniqueness of positive solutions for these kinds of problems. By converting the problem to an equivalent integral equation, then applying the new class of fixed point theorems for the sum operator on cone, we obtain the sufficient conditions which not only guarantee the existence of a unique positive solution, but also be applied to construct two iterative sequences for approximating it. Further, we present the numerical methods for solving the fourth-order differential equations. At last, some examples are given with numerical verifications to illustrate the main results.

引用

页码：1639 / 1662

页数：24

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