摘要：In this paper, we study the following max-type system of difference equations: { x n = max { A n , y n − 1 x n − 2 } , y n = max { B n , x n − 1 y n − 2 } , n ∈ { 0 , 1 , 2 , … } , $$\textstyle\begin{cases}x_{n} = \max \{A_{n},\frac{y_{n-1}}{x_{n-2}} \},\\ y_{n} = \max \{B_{n} ,\frac{x_{n-1}}{y_{n-2}} \}, \end{cases}\displaystyle n\in \{0,1,2,\ldots\}, $$ where A n , B n ∈ ( 0 , + ∞ ) $A_{n},B_{n}\in(0, +\infty)$ are periodic sequences with period 2 and the initial values x − 1 , y − 1 , x − 2 , y − 2 ∈ ( 0 , + ∞ ) $x_{-1},y_{-1},x_{-2},y_{-2}\in (0,+\infty)$ . We show that every solution of the above system is eventually periodic.
关键词：Max-type system of difference equations ; Solution ; Eventual periodicity
Loading...
