On the asymptotic behaviour of the solutions of a fifth order difference equation

TL;DR

This paper investigates the equilibrium points and the long-term asymptotic behavior of solutions to a specific fifth order difference equation, clarifying existing literature and providing new insights into its solution dynamics.

Contribution

It clarifies the equilibrium of a fifth order difference equation and thoroughly analyzes the asymptotic behavior of its solutions, extending previous studies.

Findings

Identification of equilibrium points for the equation

Characterization of asymptotic solution behavior

Insights into stability and convergence properties

Abstract

The first aim of this note is to make clear what is the equilibrium of a fifth order difference equation studied in the literature. Next the investigation of the whole asymptotic behaviour of the solutions of the equation is presented.