Abstract
In this paper we consider a spectral problem for ordinary differential equation of fourth order with a spectral parameter in the boundary conditions. This problem arises when variables are separated in the dynamical boundary value problem describing bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the both ends of which are fixed elastically and on these ends the masses are concentrated. We investigate locations, multiplicities of eigenvalues, study the oscillation properties of eigenfunctions and establish sufficient conditions for the subsystems of root functions of this problem to form a basis in the space $$L_p,\,1< p < \infty $$.
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