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

被引：15

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

页码：268 / 276

页数：9

共 11 条

[1] Sturm-Liouville problems whose leading coefficient function changes sign [J].

Cao, XF ;

Kong, QK ;

Wu, HY ;

Zettl, A .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2003, 55 (04) :724-749

[2]

Courant R., 1989, Methods of mathematical physics, V1

[3] EIGENVALUES VARIATION .1. NEUMANN PROBLEM FOR STURM-LIOUVILLE OPERATORS [J].

DAUGE, M ;

HELFFER, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (02) :243-262

[4] EIGENVALUES VARIATION .2. MULTIDIMENSIONAL PROBLEMS [J].

DAUGE, M ;

HELFFER, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (02) :263-297

[5] Eigenvalues of regular Sturm-Liouville problems [J].

Kong, Q ;

Zettl, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 131 (01) :1-19

[6] Dependence of eigenvalues of Sturm-Liouville problems on the boundary [J].

Kong, Q ;

Zettl, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 126 (02) :389-407

[7]

Kong Q, 2000, P ROY SOC EDINB A, V130, P561

[8]

Kong QK, 2008, P ROY SOC EDINB A, V138, P323

[9] Dependence of the nth Sturm-Liouville eigenvalue on the problem [J].

Kong, QK ;

Wu, HY ;

Zettl, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 156 (02) :328-354

[10] The classification of self-adjoint boundary conditions: Separated, coupled, and mixed [J].

Wang, Aiping ;

Sun, Jiong ;

Zettl, Anton .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (06) :1554-1573

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