Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 83, 2004 - Issue 3
Submit an article Journal homepage
42
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

On the difference equation xn+1 = Af(xn) + f(xn−1)

G.L. Karakostas Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece; Matemati[cbreve]ki Fakultet, Studentski Trg 16, 11000 Beograd, Serbia
&
S. Stević † Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece; Matemati[cbreve]ki Fakultet, Studentski Trg 16, 11000 Beograd, SerbiaView further author information
Pages 309-323 | Received 01 Aug 2003, Published online: 20 Aug 2006
 
Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days

Abstract

The difference equation

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.

Notes

Additional information

Notes on contributors

S. Stević Footnote†

†E-mail: [email protected]; [email protected]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.