Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 243291, 6 pages
doi:10.1155/2008/243291

On the asymptotic behavior of a difference equation with maximum

Abstract

We study the asymptotic behavior of positive solutions to the difference equation xn=max{A/xn-1α,B/xn−2β}, n=0,1,…, where 0<α, β<1, A,B>0. We prove that every positive solution to this equation converges to x∗=max{A1/(α+1),B1/(β+1)}.