Necessary and sufficient condition for oscillation of higher order nonlinear delay difference equations

This paper is concerned with the oscillation of solutions of higher order nonlinear delay difference equations with forcing terms of the form δnx(t)+f(t,x(t),x(σ(t)))=h(t), tεI={0, 1, …}, where Δ is the forward difference operator defined by Δx(t) = x(t + 1) − x(t) and Δmx(t) = Δ(Δm−1x(t)), m> 1. A necessary and sufficient condition is established under which every solution x(t) is oscillatory when n is even, and is either oscillatory or strongly monotone when n is odd. A sufficient condition for the oscillation of solutions of neutral type delay difference equations is also obtained.