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http://dx.doi.org/10.5666/KMJ.2010.50.1.153

The Dynamics of Solutions to the Equation $x_{n+1}=\frac{p+x_{n-k}}{q+x_n}+\frac{x_{n-k}}{x_n}$  

Xu, Xiaona (Department of Mathematics, Sun Yat-Sen University)
Li, Yongjin (Department of Mathematics, Sun Yat-Sen University)
Publication Information
Kyungpook Mathematical Journal / v.50, no.1, 2010 , pp. 153-164 More about this Journal
Abstract
We study the global asymptotic stability, the character of the semicycles, the periodic nature and oscillation of the positive solutions of the difference equation $x_{n+1}=\frac{p+x_{n-k}}{q+x_n}+\frac{x_{n-k}}{x_n}$, n=0, 1, 2, ${\cdots}$. where p, q ${\in}$ (0, ${\infty}$), q ${\neq}$ 2, k ${\in}$ {1, 2, ${\cdots}$} and the initial values $x_{-k}$, ${\cdots}$, $x_0$ are arbitrary positive real numbers.
Keywords
Difference equations; Asymptotic stability; Periodicity; Semicycle; Oscillation;
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