Spectral properties of a fourth-order differential operator with eigenvalue parameter-dependent boundary conditions

DOI10.1007/s40840-021-01216-6zbMath1485.34087OpenAlexW4205225899MaRDI QIDQ2117569

Vuqar A. Mehrabov

Publication date: 21 March 2022

Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40840-021-01216-6

zbMATH Keywords

eigenvalueroot functionsunconditional basisspectral problemhomogeneous rod

Mathematics Subject Classification ID

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) 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 (1)

An inverse three spectra problem for parameter-dependent and jumps conformable Sturm-Liouville operators

Cites Work

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• Eigenvalues of discrete Sturm-Liouville problems with eigenparameter dependent boundary conditions
• Basis properties of the system of eigenfunctions in the Sturm-Liouville problem with a spectral parameter in the boundary conditions
• Basis properties in \(L_{p}\) of systems of root functions of a spectral problem with spectral parameter in a boundary condition
• Basis properties of a fourth order differential operator with spectral parameter in the boundary condition
• Eigenvalues of a linear fourth-order differential operator with squared spectral parameter in a boundary condition
• On the singularities of the root space of a spectral problem with a spectral parameter in the boundary condition
• Defect basis property of a system of root functions of a Sturm-Liouville problem with spectral parameter in the boundary conditions
• On the basis property of the system of eigenfunctions of a spectral problem with spectral parameter in the boundary condition
• A Pruefer transformation for the equation of a vibrating beam subject to axial forces
• Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions
• Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load
• A boundary value problem for the Dirac system with a spectral parameter in the boundary conditions
• A Sturm-Liouville problem with physical and spectral parameters in boundary conditions
• Some properties of eigenfunctions for the equation of vibrating beam with a spectral parameter in the boundary conditions
• Spectral properties of a fourth-order eigenvalue problem with quadratic spectral parameters in a boundary condition
• Spectral properties of the equation of a vibrating rod at both ends of which the masses are concentrated
• Convergence of eigenfunction expansions for a boundary value problem with spectral parameter in the boundary conditions. I
• Convergence of eigenfunction expansions for a boundary value problem with spectral parameter in the boundary conditions. II
• On oscillation of eigenfunctions of a fourth-order problem with spectral parameters in the boundary conditions
• On a spectral problem arising in a mathematical model of torsional vibrations of a rod with pulleys at the ends
• Regular eigenvalue problems with eigenvalue parameter in the boundary condition
• Uniform convergence of Fourier series expansions for a fourth-order spectral problem with boundary conditions depending on the eigenparameter
• Self-adjoint fourth order differential operators with eigenvalue parameter dependent boundary conditions
• Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
• Sturm–Liouville problems with eigenparameter dependent boundary conditions
• On a fourth-order problem with spectral and physical parameters in the boundary condition
• Application of two parameter eigencurves to Sturm–Liouville problems with eigenparameter-dependent boundary conditions
• Spectra of a discrete Sturm-Liouville problem with eigenparameter-dependent boundary conditions in Pontryagin space
• Oscillation and basis properties for the equation of vibrating rod at one end of which an inertial mass is concentrated
• The basis property in \(L_p\) of the system of eigenfunctions corresponding to two problems with a spectral parameter in the boundary condition

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