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Bull. Korean Math. Soc. 2007; 44(3): 439-445

Printed September 1, 2007

Copyright © The Korean Mathematical Society.

Global asymptotic stability of a higher order difference equation

Alaa E. Hamza and R. Khalaf-Allah

Cairo University, Helwan University

Abstract

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The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation \[x_{n+1}=\frac{Ax_{n-1}}{B+Cx_{n-2l}x_{n-2k}},\qquad n=0,1,2,\ldots,\] where $A,B,C$ are nonnegative real numbers and $l,k$ are nonnegative integers, $l\leq k$.

Keywords: difference equation, periodic solution, globally asymptotically stable

MSC numbers: 39A11

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