Boundedness character of a max-type system of difference equations of second order

Abstract

The boundedness character of positive solutions of the next max-type system of difference equations $$x_{n+1}=\max\left\{A,\frac{y_n^p}{x_{n-1}^q}\right\},\quad y_{n+1}=\max\left\{A,\frac{x_n^p}{y_{n-1}^q}\right\},\quad n\in\mathbb{N}_0,$$ with $\min\{A, p, q\}>0$, is characterized.

Keywords

• max-type system of difference equations
• positive solutions
• bounded solutions
• unbounded solutions