On the solutions of a second order difference equation

Abstract

In this paper, we discuss the global behavior of all solutions of the difference equation Xn+1 = XnXn-1 axn + bxn-1, n € N0, where a; b are real numbers and the initial conditions X-1, X0 are real numbers. We determine the forbidden set and give an explicit formula for the solutions. We show the existence of periodic solutions, under certain conditions.

Keywords

• difference equation
• forbidden set
• periodic solution
• unbounded solution