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Zbl 1199.39025
Zayed, E.M.E.; El-Moneam, M.A.
On the rational recursive sequence $x_{n+1}=\Big ( A+\sum _{i=0}^{k}\alpha _{i}x_{n-i}\Big ) \Big / \sum _{i=0}^{k}\beta _{i}x_{n-i}$. (English)
[J] Math. Bohem. 133, No. 3, 225-239 (2008). ISSN 0862-7959

Summary: The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation $$ x_{n+1}=\bigg ( A+\sum _{i=0}^{k}\alpha _{i}x_{n-i}\bigg ) \Big / \sum _{i=0}^{k}\beta _{i}x_{n-i},\ \ n=0,1,2,\dots $$ where the coefficients $A$, $\alpha _{i}$, $\beta _{i}$ and the initial conditions $x_{-k},x_{-k+1},\dots ,x_{-1},x_{0}$ are positive real numbers, while $k$ is a positive integer number.

MSC 2000:: *39A22
39A20 Generalized difference equations
39A30
39A23

Keywords: boundedness character; period two solution; convergence; global stability; rational difference equation; positive solutions

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Zentralblatt MATH Berlin [Germany]