Eigenvalues of Fourth-Order Boundary Value Problems with Self-Adjoint Canonical Boundary Conditions

被引：8
作者：
Lv, Xiao-xia [1 ]
Ao, Ji-jun [1 ]
机构：
[1] Inner Mongolia Univ Technol, Coll Sci, Hohhot 010051, Peoples R China
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Fourth-order boundary value problems; Eigenvalues; Differential expression; Self-adjoint canonical boundary conditions; STURM-LIOUVILLE PROBLEMS; DEPENDENCE;
D O I：
10.1007/s40840-018-00714-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Fourth-order boundary value problems with general real self-adjoint boundary conditions are investigated. It is obtained that the eigenvalues of the problem depend not only continuously on all parameters of the problem but also smoothly on the boundary conditions. Furthermore, the derivatives of the eigenvalues with respect to boundary conditions are given in the sense of the fundamental canonical forms of fourth-order self-adjoint boundary conditions including each type of separated, mixed and coupled cases.
引用
收藏
页码：833 / 846
页数：14
相关论文
共 22 条
  • [1] [Anonymous], 1993, Results Math, DOI DOI 10.1007/BF03323127
  • [2] Qualitative analysis of eigenvalues and eigenfunctions of one boundary value-transmission problem
    Aydemir, Kadriye
    Mukhtarov, Oktay S.
    [J]. BOUNDARY VALUE PROBLEMS, 2016, : 1 - 16
  • [3] Bailey P.B., 2012, ELECT J DIFFERENTIAL, V2012, P1
  • [4] Algorithm 810: The SLEIGN2 Sturm-Liouville code
    Bailey, PB
    Everitt, WN
    Zettl, A
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2001, 27 (02): : 143 - 192
  • [5] EIGENVALUES VARIATION .1. NEUMANN PROBLEM FOR STURM-LIOUVILLE OPERATORS
    DAUGE, M
    HELFFER, B
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (02) : 243 - 262
  • [6] Dependence of eigenvalues of a class of fourth-order Sturm-Liouville problems on the boundary
    Ge, Suqin
    Wang, Wanyi
    Suo, Jianqing
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 220 : 268 - 276
  • [7] Algorithm 775: The code SLEUTH for solving fourth-order Sturm-Liouville problems
    Greenberg, L
    Marletta, M
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1997, 23 (04): : 453 - 493
  • [8] Canonical forms of self-adjoint boundary conditions for differential operators of order four
    Hao, Xiaoling
    Sun, Jiong
    Zettl, Anton
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 387 (02) : 1176 - 1187
  • [9] Solvability of fourth-order Sturm-Liouville problems with abstract linear functionals in boundary-transmission conditions
    Kandemir, Mustafa
    Mukhtarov, Oktay Sh
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (10) : 3643 - 3652
  • [10] Dependence of eigenvalues on the problem
    Kong, Q
    Wu, H
    Zettl, A
    [J]. MATHEMATISCHE NACHRICHTEN, 1997, 188 : 173 - 201
123