On the nonautonomous difference equation xn+1=An+xn-1pxnq

In this paper we study the asymptotic behavior and the periodicity of the positive solutions of the nonautonomous difference equation:xn+1=An+xn-1pxnq,n=0,1,…,where An is a positive bounded sequence, p, q ∈ (0, ∞) and x−1, x0 are positive numbers.