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.
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页码：2639 / 2647
页数：9
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