The existence and the uniqueness of symmetric positive solutions for a fourth-order boundary value problem

被引：36

作者：

Zhai, Chengbo ^{[1
]}

Song, Ruipeng ^{[1
]}

Han, Qianqian ^{[1
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 06期

关键词：

Fourth-order boundary value problem; Symmetric positive solution; The existence and the uniqueness; Fixed point theorem of general alpha-concave operators; EIGENVALUE PROBLEMS; EQUATIONS;

D O I：

10.1016/j.camwa.2011.08.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to investigate the existence and the uniqueness of symmetric positive solutions for a class of fourth-order boundary value problem: {y((4))(t) = f(t, y(t)), t is an element of [0, 1], y(0) = y(1) = y'(0) = y'(1) = 0. By using the fixed point index method, we establish the existence of at least one or at least two symmetric positive solutions for the above boundary value problem. Further, by using a fixed point theorem of general alpha-concave operators, we also present criteria which guarantee the existence and uniqueness of symmetric positive solutions for the above boundary value problem. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：2639 / 2647

页数：9

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