On the oscillation of partial difference equations generated by deviating arguments

Abstract

We offer sufficient conditions for the oscillation of all solutions of the partial difference equations y(m - 1, n) + β(m, n)y(m, n - 1) - δ(m, n)y(m, n) + P(m, n, y(m + k, n + l)) = Q(m, n, y(m + k, n + l)) and y(m - 1, n) + β(m, n)y(m, n -1) - δ(m, n)y(m, n) + ∑r i=1 Pi(m, n, y(m, + ki, n + li)) = ∑r i=1 Qi (m, n, y(m + ki, n + li)). Several examples which dwell upon the importance of our results are also included.