Notes on the non-autonomous Lyness equation

We prove that the solutions of the non-autonomous Lyness equation xn+1 = (xn +bn)/xn−1, bn > 0, x0 > 0, x1 > 0, are bounded away from zero and infinity if the sequence bn is monotonic. We also give an example to show that the solutions need not be bounded even when the sequence bn attains only two values.  2004 Elsevier Inc. All rights reserved