Global Behavior of the Difference Equation xn+1=xn-1g(xn)
Joint Authors
Wu, Hui
Xi, Hongjian
Sun, Taixiang
Qin, Bin
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-03
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
We consider the following difference equation xn+1=xn-1g(xn), n=0,1,…, where initial values x-1,x0∈[0,+∞) and g:[0,+∞)→(0,1] is a strictly decreasing continuous surjective function.
We show the following.
(1) Every positive solution of this equation converges to a,0,a,0, …, or 0,a,0,a,… for some a∈[0,+∞).
(2) Assume a∈(0,+∞).
Then the set of initial conditions (x-1,x0)∈(0,+∞)×(0,+∞) such that the positive solutions of this equation converge to a,0,a,0,…, or 0,a,0,a,… is a unique strictly increasing continuous function or an empty set.
American Psychological Association (APA)
Xi, Hongjian& Sun, Taixiang& Qin, Bin& Wu, Hui. 2014. Global Behavior of the Difference Equation xn+1=xn-1g(xn). Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-1014619
Modern Language Association (MLA)
Xi, Hongjian…[et al.]. Global Behavior of the Difference Equation xn+1=xn-1g(xn). Abstract and Applied Analysis No. 2014 (2014), pp.1-5.
https://search.emarefa.net/detail/BIM-1014619
American Medical Association (AMA)
Xi, Hongjian& Sun, Taixiang& Qin, Bin& Wu, Hui. Global Behavior of the Difference Equation xn+1=xn-1g(xn). Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-1014619
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014619