On the oscillatory behaviour of a class of nonlinear delay difference equations of second order

Abstract

In this paper, sufficient conditions have been obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form $$ \Delta \left( {r\left( n \right)\Delta \left( {y\left( n \right) + p\left( n \right)y\left( {n - m} \right)} \right)} \right) + q\left( n \right)G\left( {y\left( {n - k} \right)} \right) = 0 $$ under various ranges of p(n). The nonlinear function G,G ∈ C(ℝ,ℝ) is either sublinear or superlinear satisfying the condition xG(x) > 0 for x ≠ 0.