SPECTRAL PROPERTIES FOR THE EQUATION OF VIBRATING BEAM WITH A SPECTRAL PARAMETER IN THE BOUNDARY CONDITIONS

In this paper we consider the spectral problem for ordinary differential equation of fourth order with a spectral parameter in the boundary conditions. This problem arises when describing the bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is rigidly fixed, and the inertial mass is concentrated on the right end and also at this end a tracking force acts. We study the location of eigenvalues on the real axis, find the multiplicities of all eigenvalues, examine the oscillation properties of eigenfunctions and establish sufficient conditions for the subsystems of root functions of this problem to form a basis in L-p, 1 < p < infinity.