The oscillation of systems of difference equations

In this paper, sufficient conditions are established so that all bounded so lutions of the linear system of difference equations (-1)(m+1)Delta(m)y(i)(n) + Sigma(j=1)(N) q(ij)y(j)(n - tau(jj)) = 0, m grea ter than or equal to 1, i=1,...,N to be oscillatory, where q(ij) are real numbers and tau(jj) ase positive in tegers. We shall also study the oscillatory behavior of all bounded solutio ns of the linear systems of neutral difference equations of the form (-1)(m+1)Delta(m)(y(i)(n) + cy(i)(n-sigma)) + Sigma(j=1)(N) q(ij)y(j) (n - tau) = 0, m greater than or equal to 1, i=1,...,N, where c is real number and sigma and tau are positive integers. (C) 2000 El sevier Science Ltd. All rights reserved.