Asymptotic Behavior and Oscillation of Delay Partial Difference Equations with Positive and Negative Coefficients

Abstract

We obtain sufficient conditions for the oscillation of all solutions of the linear partial difference equations with positive and negative coefficients of the form A m-1,n + A m,n-1 - A mn + pA m+k - qA m+k' = 0, n+1 n+l' and A m-1,n + A m,n-1 - A mh + p mn A m+k - q mn A m+k' = 0, n+l n+l' where m,n = 0, 1,..., and k, k', l', l are nonnegative integers p, q ∈ (0, oo), and coefficients {q mn } and {p mn } are sequences of nonnegative real numbers. In this paper A mn = A m,n .