The authors consider the difference equation
where is positive and periodic with period . The initial conditions are positive. In the case it is proved that there are no solutions of odd period; then stability by the first approximation of the equilibrium is considered. Further global results are given for an associated system of three difference equations. This will lead to a global stability result for the basic equation.
Next, sufficient conditions for the existence of unbounded solutions are given. In the case the following results are obtained: existence of a unique positive equilibrium using such classical results as Theorems of Descartes and Rolle; this equilibrium is stable by the first approximation. Existence of unbounded solutions is obtained also in this case.