Some properties of eigenfunctions for the equation of vibrating beam with a spectral parameter in the boundary conditions.

In this paper we consider a spectral problem for ordinary differential equations of fourth order with the spectral parameter contained in three of the boundary conditions. We study the oscillatory properties of the eigenfunctions and, using these properties, we obtain sufficient conditions for the system of eigenfunctions of the problem in question to form a basis in the space L p (0 , 1) , 1 < p < ∞ , after removing three functions. [ABSTRACT FROM AUTHOR]