On the rational recursive sequence [formula omitted] for small [formula omitted

Abstract

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 ∈ ( 0 , ∞ ) and m ∈ { 2 , 3 , 4 , … } . In particular, we show that for sufficiently small A > 0 , there exist periodic solutions with prime period 2 m + U m + 1 , for almost all m , where U m = max { i ∈ N : i ( i + 1 ) ≤ 2 ( m − 1 ) } .