Periodic solutions for a class of nonlinear discrete Hamiltonian systems via critical point theory

In this paper, we study the multiple existence of periodic solutions of the discrete n-dimensional Hamiltonian system [image omitted] with V periodic both in t and the components of q. By showing that the action functional of this Hamiltonian system is invariant under the action of the non-compact group [image omitted], we construct a new functional for which the Palais-Smale condition holds and prove multiple existence of periodic solutions of this system via Ljusternik-Schnirelmann category theory and Morse theory.