Solvability of a nonlinear fifth-order difference equation

Abstract

Some formulas for well-defined solutions to four very special cases of a nonlinear fifth-order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth-order difference equation previously publish in this journal.