The recursive sequence xn+1 = g(xn, xn-1)/(A + xn)

Abstract

In this note, we investigate the periodic character of solutions of the nonlinear, second-order difference equation xn+1 = g(xn, xn-1)/A + xn, where the parameter A and the initial conditions x0 and x1 are positive real numbers. We give sufficient conditions under which every positive solution of this equation converges to a period two solution.