Multiple solutions of some boundary value problems with parameters

被引：5
|
作者：
Feng, Xiaojing [1 ]
Niu, Pengcheng [1 ]
Guo, Qianqiao [1 ]
机构：
[1] NW Polytech Univ, Dept Appl Math, Xian 710072, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Boundary value problem; Critical group; Morse theory; ORDINARY DIFFERENTIAL-EQUATIONS; 4TH-ORDER BEAM EQUATIONS; POSITIVE SOLUTIONS; EXISTENCE;
D O I：
10.1016/j.na.2010.09.043
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence and multiplicity of nontrivial solutions for the following second-order Dirichlet nonlinear boundary value problem with odd order derivative: -u''(t) + au'( t) + bu(t) = f(t,u( t)) for all t epsilon [0, 1] with u( 0) = u( 1) = 0, where a, b epsilon R-1, f epsilon C-1([0, 1] x R-1, R-1). By using the Morse theory, we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution, two nontrivial solutions and infinitely many solutions, separately. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1119 / 1131
页数：13
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