Matrix representations of Sturm-Liouville problems with transmission conditions

被引：25

作者：

Ao, Ji-jun ^{[1
,2
]}

Sun, Jiong ^{[1
]}

Zhang, Mao-zhu ^{[1
,3
]}

机构：

[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China

[2] Inner Mongolia Univ Technol, Coll Sci, Hohhot 010051, Peoples R China

[3] Taishan Univ, Sch Math & Syst Sci, Tai An 271021, Shandong, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2012年 / 63卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Sturm-Liouville problems; Transmission condition; Matrix eigenvalue problems; Finite spectrum; EIGENVALUE;

D O I：

10.1016/j.camwa.2012.01.051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We identify a class of Sturm-Liouville equations with transmission conditions such that any Sturm-Liouville problem consisting of such an equation with transmission condition and an arbitrary separated or real coupled self-adjoint boundary condition has a representation as an equivalent finite dimensional matrix eigenvalue problem. Conversely, given any matrix eigenvalue problem of certain type and an arbitrary separated or real coupled self-adjoint boundary condition and transmission condition, we construct a class of Sturm-Liouville problems with this specified boundary condition and transmission condition, each of which is equivalent to the given matrix eigenvalue problem. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：1335 / 1348

页数：14

共 13 条

[1]

[Anonymous], 2005, MATH SURVEYS MONOGRA

[2] The finite spectrum of Sturm-Liouville problems with transmission conditions [J].

Ao, Ji-jun ;

Sun, Jiong ;

Zhang, Mao-zhu .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (04) :1166-1173

[3]

Atkinson FV., 1964, Discrete and Continuous Boundary Value Problems

[4] Sturm-Liouville problems with impulse effects [J].

Chanane, B. .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (01) :610-626

[5]

Evertt WN., 1976, QUAEST MATH, V3, P507

[6] Sturm-Liouville problems with discontinuities at two points [J].

Kadakal, M. ;

Mukhtarov, O. Sh. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (11-12) :1367-1379

[7] Sturm-Liouville problems with finite spectrum [J].

Kong, Q ;

Wu, O ;

Zettl, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 263 (02) :748-762

[8] Inverse Sturm-Liouville problems with finite spectrum [J].

Kong, Qingkai ;

Zettl, Anton .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 386 (01) :1-9

[9] The study of Jacobi and cyclic Jacobi matrix eigenvalue problems using Sturm-Liouville theory [J].

Kong, Qingkai ;

Zettl, Anton .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (07) :1648-1655

[10] Matrix Representations of Sturm-Liouville Problems with Finite Spectrum [J].

Kong, Qingkai ;

Volkmer, Hans ;

Zettl, Anton .

RESULTS IN MATHEMATICS, 2009, 54 (1-2) :103-116

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