Oscillation for second-order nonlinear neutral delay difference equations

Using the Riccati transformation techniques, we will extend some oscillation criteria of [Appl. Math. Comput. 146 (2003) 791] and [Appl. Math. Comput. 142 (2003) 99] to the second-order nonlinear neutral delay difference equationΔ(an(Δ(xn+pnxn−τ))γ)+f(n,xn−σ)=0,n=0,1,2,…in the case when 0<γ<1, which answers a question posed by Saker [Appl. Math. Comput. 142 (2003) 99]. Two examples are considered to illustrate our main results.