Global Asymptotic Stability of a Family of Nonlinear Difference Equations

Abstract EN

In this note, we consider global asymptotic stability of the following nonlinear difference equation xn=(∏i=1v(xn-kiβi+1)+∏i=1v(xn-kiβi-1))/(∏i=1v(xn-kiβi+1)-∏i=1v(xn-kiβi-1)), n=0,1,…, where ki∈ℕ (i=1,2,…,v), v≥2, β1∈[-1,1], β2,β3,…,βv∈(-∞,+∞), x-m,x-m+1,…,x-1∈(0,∞), and m=max1≤i≤v{ki}.

Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al.

(2007).