Oscillation in neutral delay difference equations with variable coefficients

In this paper, we consider the neutral delay difference equation δ(yn−PnYn−k)+qnYn−ℓ=0, N=0,1,2,… where pn, qn (n = 0, 1, 2, …) are real numbers with pn ≥ 0, qn ≥ 0, k and ℓ are nonnegative integers. We establish some sufficient conditions for the oscillation of all solutions of (1) without the condition