Oscillation for second-order nonlinear neutral delay difference equations

Abstract

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 equation Δ(a n( Δ(x n+p nx n−τ)) γ)+f(n,x n−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.