Dependence of eigenvalues of a class of fourth-order Sturm-Liouville problems on the boundary

被引：16
|
作者：
Ge, Suqin [1 ]
Wang, Wanyi [1 ]
Suo, Jianqing [1 ]
机构：
[1] Inner Mongolia Univ, Dept Math, Hohhot 010021, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 220卷
关键词：
Fourth-order Sturm-Liouville problems; Boundary condition; Eigenvalues; OPERATORS;
D O I：
10.1016/j.amc.2013.06.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the dependence of eigenvalues of a class of fourth-order Sturm-Liouville problems on the boundary. We show that the eigenvalues depend not only continuously but smoothly on boundary points, and that the derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. In addition, we prove that as the length of the interval shrinks to zero all higher fourth-order Dirichlet eigenvalues march off to plus infinity, this is also true for the first (i.e., lowest) eigenvalue. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：268 / 276
页数：9
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