On the rational recursive sequence yn = A + yn-1yn-m for small A

This work studies the existence of positive prime periodic solutions of higher order for rational recursive equations of the form y(n) = A + y(n-1)/y(n-m), n = 0, 1, 2,.... with y(-m), y(-m+1),....y(-1) epsilon (0,infinity) and m epsilon {2, 3, 4,...}. In particular, we show that for sufficiently small A > 0, there exist periodic solutions with prime period 2m + U-m + 1, for almost all m, where U-m = max{i epsilon N : i(i + 1) <= 2(m - 1)}. (c) 2007 Elsevier Ltd. All rights reserved.