A group theory approach towards some higher order difference equations, solutions, periodicity and asymptotic behavior

Abstract

In this paper, we apply a group theory method to derive the generators of the Lie algebra for a class of (k+1)th order difference equations. We then find solutions to the difference equations and study periodicity by giving sufficient conditions for existence of certain periodicities. We further look at the asymptotic behaviour of solutions satisfying certain properties. Our results generalise some known results in the literature.