Sturm theory for the equation of vibrating beam

DOI10.1016/j.jmaa.2008.07.055zbMath1163.34330OpenAlexW1967757921MaRDI QIDQ952139

Jamel Ben Amara

Publication date: 6 November 2008

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.07.055

zbMATH Keywords

oscillation theoryfourth-order eigenvalue problemSturm theory

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Linear boundary value problems for ordinary differential equations (34B05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (14)

Spectral properties of a fourth-order eigenvalue problem with quadratic spectral parameters in a boundary condition ⋮ Oscillation properties for the equation of vibrating beam with irregular boundary conditions ⋮ New results and applications on the existence results for nonlinear coupled systems ⋮ A model of deformations of a beam with nonlinear boundary conditions ⋮ Indexing of eigenvalues of boundary value problems for Hamiltonian systems of ordinary differential equations ⋮ Spectral properties of the differential operators of the fourth-order with eigenvalue parameter dependent boundary condition ⋮ An efficient technique for finding the eigenvalues and the eigenelements of fourth-order Sturm-Liouville problems ⋮ A second-order boundary value problem with nonlinear and mixed boundary conditions: existence, uniqueness, and approximation ⋮ Nodal solutions of a nonlinear eigenvalue problem of the Euler-Bernoulli equation ⋮ Basis properties of a fourth order differential operator with spectral parameter in the boundary condition ⋮ Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load ⋮ Spectral parameter power series for fourth-order Sturm-Liouville problems ⋮ Spectral properties of a fourth order eigenvalue problem with spectral parameter in the boundary conditions ⋮ On using Bernstein scheme for computation of the eigenvalues of fourth-order Sturm-Liouville problems

Cites Work

• A Pruefer transformation for the equation of a vibrating beam subject to axial forces
• One-dimensional boundary-value problems with operators not reducing the number of changes of sign. II
• On the Oscillation of Solutions of Self-Adjoint Linear Differential Equations of the Fourth Order
• A Prufer Transformation for the Equation of the Vibrating Beam
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