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

[31] A BOUNDARY VALUE PROBLEM FOR ELLIPTIC-DIFFERENTIAL OPERATOR EQUATIONS WITH A SPECTRAL PARAMETER IN THE EQUATION AND IN THE BOUNDARY CONDITIONS
Kurbanova, Nargul K.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2015, 41 (01): : 63 - 76
[32] Inverse spectral problems for differential pencils with boundary conditions dependent on the spectral parameter
Wang, Yu Ping
Yurko, V. A.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (08) : 3190 - 3196
[33] An inverse spectral problem for the Euler-Bernoulli equation for the vibrating beam
Papanicolaou, VG
Kravvaritis, D
INVERSE PROBLEMS, 1997, 13 (04) : 1083 - 1092
[34] Basis Properties of Root Functions of Differential Operators with Spectral Parameter in the Boundary Conditions
A. A. Shkalikov
Differential Equations, 2019, 55 : 631 - 643
[35] Basis Properties of Root Functions of Differential Operators with Spectral Parameter in the Boundary Conditions
Shkalikov, A. A.
DIFFERENTIAL EQUATIONS, 2019, 55 (05) : 631 - 643
[36] Basis properties of the root functions of an eigenvalue problem with a spectral parameter in the boundary conditions
Z. S. Aliev
Doklady Mathematics, 2010, 82 : 583 - 586
[37] Basis Properties of the Root Functions of an Eigenvalue Problem with a Spectral Parameter in the Boundary Conditions
Aliev, Z. S.
DOKLADY MATHEMATICS, 2010, 82 (01) : 583 - 586
[38] On basis properties of root functions of a boundary value problem containing a spectral parameter in the boundary conditions
Aliev, Z. S.
DOKLADY MATHEMATICS, 2013, 87 (02) : 137 - 139
[39] On basis properties of root functions of a boundary value problem containing a spectral parameter in the boundary conditions
Z. S. Aliev
Doklady Mathematics, 2013, 87 : 137 - 139
[40] Spectral modeling of vibrating plates with general shape and general boundary conditions
Catania, Giuseppe
Sorrentino, Silvio
JOURNAL OF VIBRATION AND CONTROL, 2012, 18 (11) : 1607 - 1623

← 1 2 3 4 5 →