Basis properties of a fourth order differential operator with spectral parameter in the boundary condition

DOI10.2478/s11533-010-0002-yzbMath1207.34112OpenAlexW1977290209MaRDI QIDQ708001

Ziyatkhan S. Aliyev

Publication date: 8 October 2010

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-010-0002-y

zbMATH Keywords

fourth order eigenvalue problemspectral parameter in the boundary conditionbasis properties of the system of eigenfunctionsoscillation properties of eigenfunctions

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (18)

Spectral properties of a fourth-order eigenvalue problem with quadratic spectral parameters in a boundary condition ⋮ Uniform convergence of the Fourier series expansions in the subsystems of root functions of some spectral problem for ordinary differential equations of fourth order ⋮ Uniform convergence of Fourier series expansions for a fourth-order spectral problem with boundary conditions depending on the eigenparameter ⋮ Basis properties in \({L}_{p}\) of root functions of Sturm-Liouville problem with spectral parameter-dependent boundary conditions ⋮ Convergence of eigenfunction expansions for a boundary value problem with spectral parameter in the boundary conditions. I ⋮ Asymptotics of the eigenvalues of a two-term fourth-order operator with boundary conditions dependent on the spectral parameter ⋮ Some properties of eigenfunctions for the equation of vibrating beam with a spectral parameter in the boundary conditions ⋮ On oscillation properties of self-adjoint boundary value problems of fourth order ⋮ On the spectral problem arising in the mathematical model of bending vibrations of a homogeneous rod ⋮ Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load ⋮ Manypoint boundary value problems for elliptic differential-operator equations with interior singularities ⋮ Basis properties of root functions of differential operators with spectral parameter in the boundary conditions ⋮ Uniform convergence of spectral expansions for a problem with a boundary condition depending on a spectral parameter ⋮ The geometry of fourth-order differential operator ⋮ Spectral parameter power series for fourth-order Sturm-Liouville problems ⋮ Unnamed Item ⋮ Spectral properties of a fourth order eigenvalue problem with spectral parameter in the boundary conditions ⋮ Spectral properties of a fourth-order differential operator with eigenvalue parameter-dependent boundary conditions

Cites Work

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• Sturm theory for the equation of vibrating beam
• On the basis property of the system of eigenfunctions of a spectral problem with spectral parameter in the boundary condition
• Boundary problems for ordinary differential equations with parameter in the boundary conditions
• 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
• 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
• Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
• Boundary eigenvalue problems for differential equations \(N\eta=\lambda P\eta\) with \(\lambda\)-polynomial boundary conditions
• 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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