Oscillations of the system of linear nonautonomous difference equations

We consider the linear nonautonomous system of difference equations xn+1−xn+P(n)xn−k = 0, n = 0, 1, 2, . . ., where k ∈ Z, P(n) ∈ Rrxr . We obtain sufficient conditions for the system to be oscillatory. The conditions based on the eigenvalues of the matrix coefficients of the system.  2003 Elsevier Inc. All rights reserved.