On the Difference Equation xn+1=xnxn-k/(xn-k+1a+bxnxn-k)

We show that the difference equation xn+1=xnxn-k/xn-k+1(a+bxnxn-k),n∈ℕ0, where k∈ℕ, the parameters a, b and initial values x-i, i=0,k̅ are real numbers, can be solved in closed form considerably extending the results in the literature. By using obtained formulae, we investigate asymptotic behavior o...

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Bibliographic Details
Published in:Abstract and applied analysis 2012, Vol.2012 (2012), p.1-9
Main Authors: Šmarda, Zdenĕk, Iričanin, Bratislav, Diblík, Josef, Stevic, Stevo
Format: Article
Language:English
Online Access:Get full text
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Summary:We show that the difference equation xn+1=xnxn-k/xn-k+1(a+bxnxn-k),n∈ℕ0, where k∈ℕ, the parameters a, b and initial values x-i, i=0,k̅ are real numbers, can be solved in closed form considerably extending the results in the literature. By using obtained formulae, we investigate asymptotic behavior of well-defined solutions of the equation.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/108047