Ukrainian Mathematical Bulletin

Volume 4, Issue 3, 2007 pp. 365-372.

Global Asymptotic Stability of a Higher Order Difference Equation

Authors: Alaa E. Hamza, R. Khalaf-Allah
Author institution: Alaa E. Hamza, Department of Mathematics Faculty of Science, Cairo University, Giza, 12211, Egypt hamzaaeg2003@yahoo.com R. Khalaf-Allah, Department of Mathematics, Faculty of Science, Helwan University, Cairo, 11795, Egypt abuzead73@yahoo.com

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

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