Oscillation of Nonlinear Delay Partial Difference Equations

Abstract: In this paper, we consider certain nonlinear partial difference equations aAm+1,n + bAm,n+1 − cAm,n + u∑ i=1 pi(m,n)Am−σi,n−τi = 0 where a, b, c ∈ (0,∞), u is a positive integer, pi(m,n), (i = 0, 1, 2, · · ·u) are positive real sequences. σi, τi ∈ N0 = {1, 2, · · ·}, i = 1, 2, · · · , u. A new comparison theorem for oscillation of the above equation is obtained