An oscillation theorem for discrete eigenvalue problems

In this paper we consider problems that consist of symplectic difference systems depending oil all eigenvalue parameter, together with self-adjoint boundary conditions. Such symplectic difference systems contain as important cases linear Hamiltonian difference systems and also Sturm-Liouville difference equations of second and of higher order. The main result of this paper is all oscillation theorem that relates the number of eigenvalues to the number of generalized zeros of solutions.