Boundedness character of a fourth order nonlinear difference equation

In this paper, among others, we give a complete picture of the boundedness character of the positive solutions of the following nonlinear difference equationxn+1=maxA,xnpxn-3p,n∈N0,where the parameters A and p are positive real numbers. This is a natural extension of a difference equation equivalent to an equation arising in automatic control theory. We present some new methods for investigating the boundedness character of nonlinear difference equations.