Oscillation of neutral difference equations with positive and negative coefficients

In this paper, we establish some oscillation criteria for the neutral difference equation with positive and negative coefficients Δ(xn−cnxn−γ)+pnxn−τ−qnxx−σ=0(1) without the limitation of condition cn + Σn−1i=n−π + α qi ≤ 1, where cn, pn, and qn are nonnegative integers with τ − 1 ≥ maxσ,γ, γ ≥ 1, σ ≥ 0.