Oscillation problem of Left-Definite Sturm-Liouville Problems with coupled BCs

被引：2

作者：

Zhang, Yanxia ^{[1
]}

Zhang, Xuefeng ^{[2
]}

Wang, Zhongzhi ^{[1
]}

机构：

[1] AnHui Univ Technol, Sch Math & Phys, Maanshan 243002, Peoples R China

[2] AnHui Univ Technol, Dept Comp Sci, Maanshan 243002, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 18期

基金：

中国国家自然科学基金;

关键词：

Sturm-Liouville problems; Right-Definiteness; Left-Definiteness; Oscillation theory; Eigenvalue inequalities; BOUNDARY-CONDITIONS; EIGENVALUES;

D O I：

10.1016/j.amc.2013.03.054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies oscillation problems of Left-Definite regular self-adjoint SLPs with real coupled BCs. For a given eigenvalue lambda(*) of the Left-Definite SLPs with real coupled BCs, we conclude that lambda(*) is an eigenvalue of the SLPs with certain separated BCs. We also establish some inequalities among the eigenvalues for the SLPs with separated BCs and coupled BCs. With the help of the obtained results, we give an estimate of the index of eigenvalues and the number of zeros of eigenfunction for the SLPs with real coupled BCs. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

引用

页码：9709 / 9716

页数：8

共 13 条

[1] Atkinson FV., 1964, Discrete and Continuous Boundary Value Problems
[2] Regular and singular Sturm-Liouville problems with coupled boundary conditions
Bailey, PB
Everitt, WN
Zettl, A
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1996, 126 : 505 - 514
[3] Baur G., 1988, J MATH NACHR, V138, P94
[4] Inverse oscillation theory for Sturm-Liouville problems with non-separated boundary conditions
Binding, P. A.
Volkmer, H.
[J]. INVERSE PROBLEMS, 2007, 23 (01) : 343 - 355
[5] Interlacing and oscillation for Sturm-Liouville problems with separated and coupled boundary conditions
Binding, PA
Volkmer, H
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 194 (01) : 75 - 93
[6] Geometric aspects of Sturm-Liouville problems III.: Level surfaces of the nth eigenvalue
Cao, Xifang
Kong, Qingkai
Wu, Hongyou
Zettl, Anton
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 208 (01) : 176 - 193
[7] Eastham M.S.P., 1973, The spectral theory of periodic differential equations
[8] Inequalities among eigenvalues of Sturm-Liouville problems
Eastham, MSP
Kong, Q
Wu, H
Zettl, A
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 1999, 3 (01) : 25 - 43
[9] Gao Y.L., 2004, J INNER MONGOLIA U T, V23, P241
[10] Dependence of eigenvalues on the problem
Kong, Q
Wu, H
Zettl, A
[J]. MATHEMATISCHE NACHRICHTEN, 1997, 188 : 173 - 201

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