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

Abstract

In this paper, we obtain some new sufficient conditions for the existence of nontrivial m-periodic solutions of the following nonlinear difference equation Δ ( p n ( Δ x n − 1 ) δ ) + f ( n , x n ) , 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, p n+ m = p n for any n ∈ Z and f( t + m, z) = f( t, z) for any ( t, z) ∈ Z × R, (−1) δ = −1 and δ > 0.