Global asymptotic stability of a higher order difference equation

Bull. Korean Math. Soc. 2007 Vol. 44, No. 3, 439-445 Printed September 1, 2007

Alaa E. Hamza and R. Khalaf-Allah Cairo University, Helwan University

Abstract : 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, $l\leq k$.