Spectral properties of the equation of a vibrating rod at both ends of which the masses are concentrated

DOI10.1007/s43037-019-00009-1zbMath1441.34032OpenAlexW3011136842MaRDI QIDQ2175561

Ziyatkhan S. Aliyev, Faiq M. Namazov

Publication date: 29 April 2020

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s43037-019-00009-1

zbMATH Keywords

Pontryagin spacebasis property of eigenfunctionsbending vibrations of a homogeneous rodordinary differential equations of fourth order

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Eigenvalue problems for linear operators (47A75) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Linear boundary value problems for ordinary differential equations (34B05) Parameter dependent boundary value problems for ordinary differential equations (34B08) Linear operators on spaces with an indefinite metric (47B50) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (7)

Uniform convergence of the Fourier series expansions in the subsystems of root functions of some spectral problem for ordinary differential equations of fourth order ⋮ Spectral properties of a beam equation with eigenvalue parameter occurring linearly in the boundary conditions ⋮ Uniform convergence of Fourier series expansions for a fourth-order spectral problem with boundary conditions depending on the eigenparameter ⋮ Basis properties of root functions of a vibrational boundary value problem with boundary conditions depending on the spectral parameter ⋮ Unnamed Item ⋮ On the uniform convergence of Fourier series expansions in the system of eigenfunctions of the equation of a vibrating rod at one end of which the mass is concentrated ⋮ Spectral properties of a fourth-order differential operator with eigenvalue parameter-dependent boundary conditions

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