On the solutions of a max-type system of difference equations of higher order

Advances in Difference Equations

article

Su, Guangwang¹  Han, Caihong¹  Sun, Taixiang¹  Li, Lue¹ 

[1] College of Information and Statistics

关键词: Max-type system of difference equations;    Solution;    Eventual periodicity;   

DOI  :  10.1186/s13662-020-02673-2

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we study the following max-type system of difference equations of higher order: $$ \textstyle\begin{cases} x_{n} = \max \{A ,\frac{y_{n-t}}{x_{n-s}} \}, \\ y_{n} = \max \{B ,\frac{x_{n-t}}{y_{n-s}} \},\end{cases}\displaystyle \quad n\in \{0,1,2,\ldots \}, $$ where $A,B\in (0, +\infty )$, $t,s\in \{1,2,\ldots \}$ with $\gcd (s,t)=1$, the initial values $x_{-d},y_{-d},x_{-d+1},y_{-d+1}, \ldots , x_{-1}, y_{-1}\in (0,+ \infty )$ and $d=\max \{t,s\}$.

【 授权许可】

CC BY