退化的高阶差分方程周期解的存在性

The existence of periodic solution of degenerate high order difference equation

利用傅立叶级数理论,探讨了退化的高阶差分方程EX(k)=A1X(k-1)+A2X(k-2)+…+AnX(k-n)周期解存在的充要条件,给出了二维退化的二阶差分方程周期解存在的代数判别方法,并通过实例说明其应用.

This paper discusses the existence of periodic solution of degenerate high order difference equation EX（k）=A1X（k-1）＋A2X（k-2）＋…＋AnX（k-n）, and gives the algebraic method to judge the existence of periodic solution of two-dimensional degenerate two-order difference equation. An example is finally given to illustrate the main results of this paper.