A NOTE ON POSITIVE NONOSCILLATORY SOLUTIONS OF THE DIFFERENCE EQUATION

TitleA NOTE ON POSITIVE NONOSCILLATORY SOLUTIONS OF THE DIFFERENCE EQUATION
Publication TypeJournal Article
Year of Publication2008
AuthorsVAN KHUONG, VU
Volume12
Issue2
Start Page199
Pagination9
Date Published2008
ISSN1083-2564
AMS39A10
Abstract

The aim of this note is to show that the following difference equation$${ x_{n+1} = \frac{p} {x_n} + \left(\frac{x_{n−2}} {x_n} \right)^α }$$ where p, α > 0, has positive nonoscillatory solutions which converge to the positive equilibrium ${ \bar{x} = \frac {1 + \sqrt{1 + 4p}} {2} }$ . In the proof of the result we use a method developed by L. Berg and S. Stevic.

URLhttp://www.acadsol.eu/en/articles/12/2/8.pdf
Refereed DesignationRefereed
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