Authors: Karakostas, George
Stević, Stevo 
Title: On the difference equation x n +1 = Af(x n ) + f(x n −1)
Journal: International Journal of Phytoremediation
Volume: 83
Issue: 3
First page: 309
Last page: 323
Issue Date: 1-Jan-2004
Rank: M22
ISSN: 1522-6514
DOI: 10.1080/00036810310001632880
The difference equation (Formula presented.) where f : R \ {0} → R is a piecewise nonincreasing continuous function, is investigated for various values of the parameter A. If A > 0, then sufficient conditions are given to ensure that all solutions converge to the (unique) equilibrium of the equation. If A ≤ 0, it is shown that period two solutions exist and their (local) exponential stability and Lyapunov instability are discussed. Moreover in some specific cases it is shown that these periodic solutions are (globally) asymptotically stable. © 2004, Taylor & Francis Group, LLC.
Keywords: 2000 AMS Subject Classifications: 39A11 | Asymptotic properties | Difference equations | Periodic solutions | Stability
Publisher: Taylor & Francis

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