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.
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页码：1119 / 1131
页数：13
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