On the asymptotic behavior of xn+1 = anxn/xn−1

We investigate the asymptotic behavior of solutions of a separable difference equation of the form xn+1 = anxn xn−1 , n= 0, 1, . . . , where {an}∞n=0 is a sequence of nonzero real numbers and the initial conditions x−1,x0 are nonzero real numbers.  2003 Elsevier Science (USA). All rights reserved.