Electron. J. Differential Equations, Vol. 2017 (2017), No. 307, pp. 1-11.

Spectral properties of a fourth-order eigenvalue problem with spectral parameter in the boundary conditions

Ziyatkhan S. Aliyev, Faiq M. Namazov

In this article we consider eigenvalue problems for fourth-order ordinary differential equation with spectral parameter in boundary conditions. We study the location of eigenvalues on the real axis, find the multiplicities of eigenvalues, investigate the oscillation properties of eigenfunctions, and the basis properties in the space $L_p$, $1 < p < \infty$, of the subsystems of eigenfunctions of this problem.

Submitted August 29, 2017. Published December 14, 2017.
Math Subject Classifications: 34B05, 34B09, 34B24.
Key Words: Bending vibrations of a homogeneous rod; fourth order ODE; oscillation properties of eigenfunctions; basis properties of eigenfunctions.

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Ziyatkhan S. Aliyev
Baku State University
Baku AZ1148, Azerbaijan
email: z_aliyev@mail.ru
Faiq M. Namazov
Baku State University
Baku AZ1148, Azerbaijan
email: faig-namazov@mail.ru

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