Convergence of Eigenfunction Expansions for a Boundary Value Problem with Spectral Parameter in the Boundary Conditions. I

被引：12

作者：

Aliyev, Z. S. ^{[1
,2
]}

Kerimov, N. B. ^{[2
,3
]}

Mehrabov, V. A. ^{[1
]}

机构：

[1] Baku State Univ, AZ-1148 Baku, Azerbaijan

[2] Azerbaijan Natl Acad Sci, Inst Math & Mech, AZ-1141 Baku, Azerbaijan

[3] Khazar Univ, AZ-1096 Baku, Azerbaijan

来源：

DIFFERENTIAL EQUATIONS | 2020年 / 56卷 / 02期

关键词：

STURM-LIOUVILLE PROBLEM; ROOT FUNCTIONS; BASIS PROPERTY; L-P; SYSTEM; OPERATOR;

D O I：

10.1134/S0012266120020019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a spectral problem arising in the description of bending vibrations of a homogeneous rod with a longitudinal force acting in the cross sections, with clamped left end, and with a lumped inertial load at the right end. We give a general characterization of the arrangement of eigenvalues on the real line, study the structure of root subspaces and the oscillation properties of eigenfunctions, and analyze the basis properties of the eigenfunction system of this problem in the space Lp, 1 < p < infinity.

引用

页码：143 / 157

页数：15

共 31 条

[1] Defect Basis Property of a System of Root Functions of a Sturm-Liouville Problem with Spectral Parameter in the Boundary Conditions
Aliev, Z. S.
Dun'yamalieva, A. A.
[J]. DIFFERENTIAL EQUATIONS, 2015, 51 (10) : 1249 - 1266
[2] On basis properties of root functions of a boundary value problem containing a spectral parameter in the boundary conditions
Aliev, Z. S.
[J]. DOKLADY MATHEMATICS, 2013, 87 (02) : 137 - 139
[3] Basis Properties in Lp of Systems of Root Functions of a Spectral Problem with Spectral Parameter in a Boundary Condition
Aliev, Z. S.
[J]. DIFFERENTIAL EQUATIONS, 2011, 47 (06) : 766 - 777
[4] Aliyev ZS, 2015, PROC INST MATH MECH, V41, P22
[5] Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load
Aliyev, Ziyatkhan S.
Guliyeva, Sevinc B.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (09) : 5830 - 5845
[6] Aliyev ZS, 2017, MEDITERR J MATH, V14, DOI 10.1007/s00009-017-0933-7
[7] Basis properties of a fourth order differential operator with spectral parameter in the boundary condition
Aliyev, Ziyatkhan S.
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2010, 8 (02): : 378 - 388
[8] [Anonymous], 1924, Methoden der mathematischen Physik
[9] [Anonymous], 1978, VIBRATSII TEKHNIKE S
[10] AZIZOV TY, 1971, MAT ISSLED, V6, P158

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