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ON A HIGHER-ORDER RATIONAL DIFFERENCE EQUATION
BELHANNACHE, FARIDA,TOUAFEK, NOURESSADAT,ABO-ZEID, RAAFAT The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.5
In this paper, we investigate the global behavior of the solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-2k-1}}{C+D\prod_{i=l}^{k}x_{n-2i}^{m_i}}$, n=0, 1, ..., with non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and m<sub>i</sub>, i=l, k are positive integers.
On a Higher-Order Rational Difference Equation
Farida Belhannache,Nouressadat Touafek,Raafat Abo-Zeid 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5
In this paper, we investigate the global behavior of the solutions of the difference equation \begin{equation*} x_{n+1}=\frac{A+B x_{n-2k-1}}{C+D \prod^{k}_{i=l}x_{n-2i}^{m_{i}}},\text{ }n=0,1,..., \end{equation*}% with non-negative initial conditions, the parameters $A,$ $B$ are non-negative real numbers, $C$, $D$ are positive real numbers, $k,$ $l$ are fixed non-negative integers such that $l\leq k$, and $m_{i}, i=\overline{l,k}$ are positive integers.