关键词: 指数型二分性, 反周期解, Banach不动点定理

Abstract: The author considered the antiperiodic solutions for a class of nonlinear discrete systems with exponential dichotomy. Firstly, it was proved that if the homogeneous linear system had exponential dichotomy, then the corresponding nonhomogeneous linear system had an antiperiodic solution. Secondly, by means of this conclusion and the Banach fixed point theorem, a sufficient condition for the existence and uniqueness of antiperiodic solutions for nonlinear discrete systems was given. Finally, an application example was given.

Key words: exponential dichotomy, antiperiodic solution, Banach fixed point theorem