Eventually Periodic Solutions of a Max-Type Difference Equation
Joint Authors
Tao, Chunyan
Liu, Xinhe
Liu, Jing
He, Qiuli
Sun, Taixiang
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-01
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
We study the following max-type difference equation xn=max{An/xn-r,xn-k}, n=1,2,…, where {An}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 x1-d,x2-d,…,x0 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 Stevic´ (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.
American Psychological Association (APA)
Sun, Taixiang& Liu, Jing& He, Qiuli& Liu, Xinhe& Tao, Chunyan. 2014. Eventually Periodic Solutions of a Max-Type Difference Equation. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-4.
https://search.emarefa.net/detail/BIM-1048794
Modern Language Association (MLA)
Sun, Taixiang…[et al.]. Eventually Periodic Solutions of a Max-Type Difference Equation. The Scientific World Journal No. 2014 (2014), pp.1-4.
https://search.emarefa.net/detail/BIM-1048794
American Medical Association (AMA)
Sun, Taixiang& Liu, Jing& He, Qiuli& Liu, Xinhe& Tao, Chunyan. Eventually Periodic Solutions of a Max-Type Difference Equation. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-4.
https://search.emarefa.net/detail/BIM-1048794
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1048794