On the asymptotic behavior and periodic nature of a difference equation with maximum

In this paper, we investigate the asymptotic behavior and periodic nature of positive solutions of the difference equation x n = max { A x n − 1 , 1 x n − 2 α } , n ≥ 0 , where A ≥ 0 and 0 ≤ α ≤ 1 . We prove that every positive solution of this difference equation approaches x ¯ = 1 or is eventually...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2010, Vol.59 (2), p.898-902
Main Authors: Gelişken, Ali, Çinar, Cengiz, Kurbanli, Abdullah Selçuk
Format: Article
Language:English
Subjects:
Difference equation
Global attractivity
Max operator
Periodicity
Positive solution
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Summary:In this paper, we investigate the asymptotic behavior and periodic nature of positive solutions of the difference equation x n = max { A x n − 1 , 1 x n − 2 α } , n ≥ 0 , where A ≥ 0 and 0 ≤ α ≤ 1 . We prove that every positive solution of this difference equation approaches x ¯ = 1 or is eventually periodic with a period 2, 3 or 4.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2009.10.004