On a family of higher order recurrence relations: symmetries, formula solutions, periodicity and stability analysis

Abstract

Abstract In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry analysis as part of our approach together with some number theoretic functions. Our findings generalize certain results in the literature.

Keywords

• 39A10
• 39A13
• 39A99