Dynamical Behavior and Expressions of Solutions of a Class of Higher-Order Nonlinear Difference Equations

Abstract

The aim of this article is to get the forms of the solutions of the following nonlinear higher-order difference equations ${\chi }_{s+1}=\left({\chi }_{s-3k+1}/\pm 1\pm {\Pi }_{l=1}^k{\chi }_{s-3l+1}\right),s=0,1,2,\dots ,$ where the initial conditions ${\chi }_{-j},j=0,1,2,\dots ,3k-1$ and $k\in \left\{1,2,\dots \right\}$ are arbitrary real numbers. Also, we examine stability, boundedness, oscillation, and the periodic nature of these solutions.