On the solutions of a max-type system of difference equations with period-two parameters
Abstract In this paper, we study the following max-type system of difference equations: {xn=max{An,yn−1xn−2},yn=max{Bn,xn−1yn−2},n∈{0,1,2,…}, $$\textstyle\begin{cases}x_{n} = \max \{A_{n},\frac{y_{n-1}}{x_{n-2}} \},\\ y_{n} = \max \{B_{n} ,\frac{x_{n-1}}{y_{n-2}} \}, \end{cases}\displaystyle n\in \{...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1826-1 |
| Summary: | Abstract In this paper, we study the following max-type system of difference equations: {xn=max{An,yn−1xn−2},yn=max{Bn,xn−1yn−2},n∈{0,1,2,…}, $$\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 An,Bn∈(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. |
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| ISSN: | 1687-1847 |