In:
The Scientific World Journal, Hindawi Limited, Vol. 2014 ( 2014), p. 1-4
Abstract:
We study the following max-type difference equation x n = max { A n / x n - r , x n - k } , n = 1,2 , … , where { A n } n = 1 + ∞ is a periodic sequence with period p and k , r ∈ { 1,2 , … } with gcd ( k , r ) = 1 and k ≠ r , and the initial conditions x 1 - d , x 2 - d , … , x 0 are real numbers with d = max { r , k } . We show that if p = 1 (or p ≥ 2 and k is odd), then every well-defined solution of this equation is eventually periodic with period k , which generalizes the results of (Elsayed and Stevi c ´ (2009), Iričanin and Elsayed (2010), Qin et al. (2012), and Xiao and Shi (2013)) to the general case. Besides, we construct an example with p ≥ 2 and k being even which has a well-defined solution that is not eventually periodic.
Type of Medium:
Online Resource
ISSN:
2356-6140
,
1537-744X
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2014
detail.hit.zdb_id:
2075968-X
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