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 Hamiltonian system $$\Delta^{2}u(n-1)=\nabla F(n,u(n)), \quad n\in\mathbb{Z}.$$ When the nonlinear function $F(n,x)$ is like-quadratic for $x$, we obtain some existence and multiplicity results under twisting conditions by using the least action principle and a multiple critical point theorem. The methods and main ideas using in this paper are variational method and critical point theory. The twisting conditions in our results are different from that in the lituratures.

Keywords

• periodic solution
• second-order discrete Hamiltonian system
• the least action principle
• critical point theory

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