Periodic solutions of a class of nonlinear difference equations via critical point method

In this paper, we obtain some new sufficient conditions for the existence of nontrivial m-periodic solutions of the following nonlinear difference equationΔ(pn(Δxn−1)δ)+f(n,xn), n∈Z,by using the critical point method, where f: Z × R → R is continuous in the second variable, m ≥ 2 is a given positive integer, pn+m = pn for any n ∈ Z and f(t + m, z) = f(t, z) for any (t, z) ∈ Z × R, (−1)δ = −1 and δ > 0.