Existence and Multiplicity of Periodic Solutions for Nonautonomous Second-Order Discrete Hamiltonian Systems

Abstract

In this paper, we consider the periodic solutions of the following non-autonomous second order discrete system∆2u(n − 1) = ∇F(n, u(n)), n ∈ Z.When the nonlinear function F(n, x) is like-quadratic for x, we obtain some existence and multiplicity results undertwisting conditions by using the least action principle and a multiple critical point theorem.