Oscillations of higher-order of systems of difference equations

In this paper, we provide necessary and sufficient conditions for the oscillation of every solution of the system of difference equations Delta(r)y(n) + Py-n (- k) = 0, n = 0, 1, 2,..., where P is an element of R-sxs and k is an element of Z. Furthermore, we prove sufficient conditions for the oscillation of every solution of the system of difference equations Delta(r)y(n) + Sigma(m)(i=1) P(i)y(n - ki) = 0, n = 0, 1, 2,..., where P is an element of R-sxs and k(i) is an element of Z for i = 1, 2,..., m.