Bounded oscillation for second-order nonlinear neutral difference equations in critical and non-critical states

The sufficient and necessary conditions for the bounded oscillation of the second order nonlinear neutral delay difference equationΔ2[x(n)-px(n-τ)]=∑i=1mqix(n-σi)+f(n,x(n-η1(n)),…,x(n-ηl(n)))are obtained in critical and non-critical cases.