Qualitative Behavior of Solutions of Tenth-Order Recursive Sequence Equation

Abstract

Most nonlinear difference equations have exact solutions that are not always possible to obtain theoretically. As a result, a large number of researchers investigate several qualitative aspects of difference equations in order to predict their lengthy behavior. The goal of our research is to obtain the solutions of a tenth-order difference equation U n + 1 = U n − 9 U n − 5 U n − 1 / U n − 7 U n − 3 ± 1 ± U n − 9 U n − 5 U n − 1 , n ≥ 0 , where the initial values are positive real numbers. Stability and periodicity are also investigated.

On the Behavior of the Nonlinear Difference Equation yn+1 = Ayn−1 + Byn−3 + Cyn−1+Dyn−3/Fyn−3−E

“…, n = 0, 1, ... Elsayed et al [13] investigated the stability and periodicity as well as obtaining the solutions of a higher-order difference equation…”