Oscillation of Second Order Neutral Difference Inequalities with Oscillating Coefficients

In this paper, we established some sufficient conditions for the oscillation of second order neutral difference inequalities (−1)δx(n){ ∆^2 z(n) + (−1)^δ q(n)f(x(σ(n)))} ≤ 0, n ≥ n0 (∗) where δ = 0 or δ = 1, z(n) = x(n) + p(n)x(n − τ ), τ is a positive integer, {p(n)}, {q(n)} are sequences of real numbers, {σ(n)} is a sequence of nonnegative integers and f : R → R where R is the set of real numbers. There are proved sufficient conditions under which every ounded solution of (∗) is either oscillatory or lim infn→∞ |x(n)| = 0.