Periodic Solutions of a Class of Nonlinear Difference Equations via Critical Point Method

摘要

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(Δx_(n-1))~δ)+f(n,x_n)=0, n ∈Z, by using the critical point method, where f : Z x 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 x R, (-1)~δ = -1 and δ > 0.