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

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页码：2639 / 2647

页数：9

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