Solutions of the difference equation xn+1= xnx n-1-1

Abstract

Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: xn+1= x nxn-1-1, n=0,1,2,⋯, where the initial conditions x-1 and x0 are real numbers. We examine the boundedness of solutions, periodicity of solutions, and existence of unbounded solutions and how these behaviors depend on initial conditions.