On a nonlinear difference equation of the fourth order solvable in closed form and its solutions

Abstract

We show that a nonlinear difference equation recently considered in this journal is a special case of a solvable class of nonlinear difference equations and that the difference equation is closely related to a difference equation previously considered in the literature. We give some detailed theoretical explanations for the closed-form formulas for the solutions to the four special cases of the difference equation considered therein without giving any theoretical explanations related to them, and also show that several statements on the long-term behaviour of positive solutions to the difference equation given therein are not true.