The Behavior of Positive Solutions of a Nonlinear Second-Order Difference Equation
Joint Authors
Berenhaut, Kenneth S.
Stevic, Stevo
Source
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-01-02
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn=f(xn−2)/g(xn−1), n∈ℕ0, where f,g∈C[(0,∞),(0,∞)].
It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n−1} are eventually monotone.
For the case when f(x)=α+βx and g satisfies the conditions g(0)=1, g is nondecreasing, and x/g(x) is increasing, we prove that every prime periodic solution of the equation has period equal to one or two.
We also investigate the global periodicity of the equation, showing that if all solutions of the equation are periodic with period three, then f(x)=c1/x and g(x)=c2x, for some positive c1 and c2.
American Psychological Association (APA)
Stevic, Stevo& Berenhaut, Kenneth S.. 2008. The Behavior of Positive Solutions of a Nonlinear Second-Order Difference Equation. Abstract and Applied Analysis،Vol. 2008, no. 2008, pp.1-8.
https://search.emarefa.net/detail/BIM-987610
Modern Language Association (MLA)
Stevic, Stevo& Berenhaut, Kenneth S.. The Behavior of Positive Solutions of a Nonlinear Second-Order Difference Equation. Abstract and Applied Analysis No. 2008 (2008), pp.1-8.
https://search.emarefa.net/detail/BIM-987610
American Medical Association (AMA)
Stevic, Stevo& Berenhaut, Kenneth S.. The Behavior of Positive Solutions of a Nonlinear Second-Order Difference Equation. Abstract and Applied Analysis. 2008. Vol. 2008, no. 2008, pp.1-8.
https://search.emarefa.net/detail/BIM-987610
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-987610