Oscillation criteria for nonlinear second-order difference equations with a nonlinear damped term

Sufficient conditions for the oscillation of solutions of the nonlinear second-order difference equation of the form Δ[p(k)ψ(y(k))Δy(k)]+q(k)h(y(k))g(Δy(k−r(k)))Δy(k)+f(k,y(k),y(k−s1(k)),y(k−s2(k)),…,y(k−sn(k)))=0 are established. We obtain a series of results for oscillatory behaviour.