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

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 1,  2010, pp.153-164
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.1.153
Title & Authors
The Dynamics of Solutions to the Equation $\small{x_{n+1}=\frac{p+x_{n-k}}{q+x_n}+\frac{x_{n-k}}{x_n}}$
Xu, Xiaona; Li, Yongjin;

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 $\small{x_{n+1}=\frac{p+x_{n-k}}{q+x_n}+\frac{x_{n-k}}{x_n}}$, n=0, 1, 2, $\small{{\cdots}}$. where p, q $\small{{\in}}$ (0, $\small{{\infty}}$), q $\small{{\neq}}$ 2, k $\small{{\in}}$ {1, 2, $\small{{\cdots}}$} and the initial values $\small{x_{-k}}$, $\small{{\cdots}}$, $\small{x_0}$ are arbitrary positive real numbers.
Keywords
Difference equations;Asymptotic stability;Periodicity;Semicycle;Oscillation;
Language
English
Cited by
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