Periodic solutions of a class of non-autonomous second-order discrete Hamiltonian systems

Abstract

In this paper, in the view of control functions, the existence of periodic solutions of the following second-order discrete Hamiltonian system $ \bigtriangleup ^{2} u(n-1) = \nabla F(n, u(n)), \ \ n\in \mathbb{Z} $ with a generalized sublinear condition is further explored.

Keywords

• periodic solution
• control function
• the least action principle
• saddle point theorem