Matrix representations of fourth order boundary value problems with periodic boundary conditions

被引:5
作者
Ge, Suqin [1 ]
Wang, Wanyi [1 ]
Ao, Jijun [2 ]
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
关键词
Boundary value problems; Matrix representations; Eigenvalues; STURM-LIOUVILLE PROBLEMS; TRANSMISSION CONDITIONS; FINITE SPECTRUM;
D O I
10.1016/j.amc.2013.11.059
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We show that a class of regular self-adjoint fourth order boundary value problems (BVPs) is equivalent to a certain class of matrix problems. Conversely, for any given matrix problem in this class, there exist fourth order self-adjoint BVPs which are equivalent to the given matrix problem. Equivalent here means that they have exactly the same eigenvalues. Such an equivalence is considered with the special coupled boundary conditions, i.e. periodic boundary conditions. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:601 / 609
页数:9
相关论文
共 10 条
[1]  
[Anonymous], 1968, LINEAR DIFFERENTIAL
[2]   The Finite Spectrum of Sturm-Liouville Problems with Transmission Conditions and Eigenparameter-Dependent Boundary Conditions [J].
Ao, Ji-jun ;
Sun, Jiong ;
Zhang, Mao-zhu .
RESULTS IN MATHEMATICS, 2013, 63 (3-4) :1057-1070
[3]   Equivalence of Fourth Order Boundary Value Problems and Matrix Eigenvalue Problems [J].
Ao, Ji-jun ;
Sun, Jiong ;
Zettl, Anton .
RESULTS IN MATHEMATICS, 2013, 63 (1-2) :581-595
[4]   Matrix representations of Sturm-Liouville problems with transmission conditions [J].
Ao, Ji-jun ;
Sun, Jiong ;
Zhang, Mao-zhu .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (08) :1335-1348
[5]   Matrix representations of fourth order boundary value problems with finite spectrum [J].
Ao, Ji-jun ;
Sun, Jiong ;
Zettl, Anton .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (07) :2359-2365
[6]   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
[7]  
Atkinson FV., 1964, Discrete and Continuous Boundary Value Problems
[8]   Sturm-Liouville problems with finite spectrum [J].
Kong, Q ;
Wu, O ;
Zettl, A .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 263 (02) :748-762
[9]   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
[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