Basis properties of the system of eigenfunctions of a fourth order eigenvalue problem with spectral parameter in the boundary conditions

In this paper we consider the eigenvalue problem for fourth order ordinary differential equation that describes the bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is fixed rigidly, the right end is fixed elastically and on this end the inertial mass is concentrated. We investigate the location of eigenvalues on the real axis, the structure of root spaces and oscillation properties of eigenfunctions and their derivatives, we study the basis properties in the space Lp, 1 < p < ∞, of the subsystems of eigenfunctions of this problem