一类非自治离散Hamiltonian系统的周期解

Periodic solution for a class of non-autonomous discrete Hamiltonian system

研究了一阶非自治离散Hamiltonian系统周期解的存在性.在非线性项是线性增长条件时,将这类Hamilto-nian系统的周期解转化为定义在一个适当空间上泛函的临界点,然后利用临界点理论中的鞍点定理,建立了此类系统周期解的存在性结果.

In this paper,we study the existence of periodic solutions for first order non-autonomous discrete Hamiltonian system.When nonlinearity satisfies linear growth condition,we convert periodic solutions of the system into the critical points of a functional defined on a proper space and prove the existence of periodic solutions based on the saddle point theorem in the critical point theory.