Stability problem of some nonlinear difference equations - Alaa E. Hamza; M. A. El-Sayed (International Journal of Mathematics and Mathematical Sciences)
In this paper, we investigate the asymptotic stability of the recursive sequence xn+1=α+βxn21+γxn−1,    n=0,1,… and the existence of certain monotonic solutions of the equation xn+1=xnpf(xn,xn−1,…,xn−k),     n=0,1,… which includes as a special case the rational recursive sequence xn+1=βxnp1+∑i=1kγixn−1p−r,