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

Authors : Messaoud Berkal, R Abo-zeid

Pages : 136-144

Doi:10.32323/ujma.1198471

View : 14 | Download : 5

Publication Date : 2022-12-29

Article Type : Research

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.