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

Abstract

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.

Keywords

• Bending vibrations of a homogeneous rod
• fourth order ODE
• oscillation properties of eigenfunctions
• basis properties of eigenfunctions