On a Rational $(P+1)$th Order Difference Equation with Quadratic Term

Year 2022, Volume: 5 Issue: 4, 136 - 144, 29.12.2022

Messaoud Berkal , R Abo-zeıd

https://doi.org/10.32323/ujma.1198471

Cited By: 7

Abstract

In this paper, we derive the forbidden set and determine the solutions of the difference equation that contains a quadratic term \begin{equation*} x_{n+1}=\frac{x_{n}x_{n-p}}{ax_{n-(p-1)}+bx_{n-p}},\quad n\in\mathbb{N}_0, \end{equation*} where the parameters $a$ and $b$ are real numbers, $p$ is a positive integer and the initial conditions $x_{-p}$, $x_{-p+1}$, $\cdots$, $x_{-1}$, $x_{0}$ are real numbers.

Keywords

Difference equations , General solution , Forbidden set , Invariant set , convergence.

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