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
Cao, XF
Kong, QK
Wu, HY
Zettl, A
[J]. 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
DAUGE, M
HELFFER, B
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (02) : 243 - 262
[4] EIGENVALUES VARIATION .2. MULTIDIMENSIONAL PROBLEMS
DAUGE, M
HELFFER, B
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (02) : 263 - 297
[5] Eigenvalues of regular Sturm-Liouville problems
Kong, Q
Zettl, A
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 131 (01) : 1 - 19
[6] Dependence of eigenvalues of Sturm-Liouville problems on the boundary
Kong, Q
Zettl, A
[J]. 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
Kong, QK
Wu, HY
Zettl, A
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 156 (02) : 328 - 354
[10] The classification of self-adjoint boundary conditions: Separated, coupled, and mixed
Wang, Aiping
Sun, Jiong
Zettl, Anton
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (06) : 1554 - 1573

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