SPECTRAL PROPERTIES FOR THE EQUATION OF VIBRATING BEAM WITH A SPECTRAL PARAMETER IN THE BOUNDARY CONDITIONS

被引：0

作者：

Mekhrabov, Vuqar A. ^{[1
]}

机构：

[1] Baku State Univ, Z Khalilov Str 23, AZ-1148 Baku, Azerbaijan

来源：

PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS | 2019年 / 45卷 / 02期

关键词：

beam equation; spectral parameter; location of eigenvalues; basis property of root functions; STURM-LIOUVILLE PROBLEMS; EIGENVALUE PARAMETER; EIGENFUNCTIONS; SYSTEM;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the spectral problem for ordinary differential equation of fourth order with a spectral parameter in the boundary conditions. This problem arises when describing the bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is rigidly fixed, and the inertial mass is concentrated on the right end and also at this end a tracking force acts. We study the location of eigenvalues on the real axis, find the multiplicities of all eigenvalues, examine the oscillation properties of eigenfunctions and establish sufficient conditions for the subsystems of root functions of this problem to form a basis in L-p, 1 < p < infinity.

引用

页码：319 / 330

页数：12

共 50 条

[41] Spectral modeling of vibrating plates with general shape and general boundary conditions
Catania, Giuseppe
Sorrentino, Silvio
JVC/Journal of Vibration and Control, 2012, 18 (11): : 1607 - 1623
[42] SOLVABILITY OF BOUNDARY VALUE PROBLEM FOR SECOND ORDER ELLIPTIC DIFFERENTIAL-OPERATOR EQUATION WITH SPECTRAL PARAMETER IN THE EQUATION AND BOUNDARY CONDITIONS
Aliev, Bahram A.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2010, 33 (41): : 3 - 26
[43] Inverse Problem of Spectral Analysis for Diffusion Operator with Nonseparated Boundary Conditions and Spectral Parameter in Boundary Condition
Ibadzadeh, Ch G.
Mammadova, L., I
Nabiev, I. M.
AZERBAIJAN JOURNAL OF MATHEMATICS, 2019, 9 (01): : 171 - 189
[44] Spectral problems with the spectral parameter in the boundary condition
Kapustin, NY
Moiseev, EI
DIFFERENTIAL EQUATIONS, 1997, 33 (01) : 116 - 120
[45] Inverse scattering transform in squared spectral parameter for DNLS equation under vanishing boundary conditions
He Jin-Chun
Chen Zong-Yun
Yan Tian
Huang Nian-Ning
CHINESE PHYSICS LETTERS, 2008, 25 (07) : 2403 - 2406
[46] FORMULA FOR SECOND REGULARIZED TRACE OF THE STURM-LIOUVILLE EQUATION WITH SPECTRAL PARAMETER IN THE BOUNDARY CONDITIONS
Movsumova, Hajar F.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2016, 42 (01): : 93 - 105
[47] An eigenvalue problem for a nonlinear Sturm-Liouville equation with boundary conditions depending on the spectral parameter
Makin, AS
DOKLADY MATHEMATICS, 2004, 70 (03) : 870 - 873
[48] A Boundary Value Problem for the Dirac System with a Spectral Parameter in the Boundary Conditions
N. B. Kerimov
Differential Equations, 2002, 38 : 164 - 174
[49] A boundary value problem for the dirac system with a spectral parameter in the boundary conditions
Kerimov, NB
DIFFERENTIAL EQUATIONS, 2002, 38 (02) : 164 - 174
[50] Asymptotics of the eigenvalues of a boundary value problem for the operator Schrodinger equation with boundary conditions nonlinearly dependent on the spectral parameter
Hashimoglu, I. F.
VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2021, 25 (04): : 607 - 615

← 1 2 3 4 5 →