The aim of this work is to investigate the global stability, periodic nature, oscillation, and the boundedness of all admissible solutions of the difference equationxn+1=Axn-2r-1/(B-C∏i=lkxn-2i), n=0,1,2,…whereA,B,Care positive real numbers andl,r,kare nonnegative integers, such thatl≤k.

In this paper, we investigate the global behavior of the solutions of the difference equationwith non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and m i , i = l, k are positive integers.

ABSTRACT. The aim of this paper is to investigate the global stability and periodic nature of the positive solutions of the difference equationwhere A, B are nonnegative real numbers, C, D > 0 and l, k are nonnegative integers such that l ≤ k.

Abstract. In this paper, we discuss the global behavior of all solutions of the difference equationwhere 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.

In this paper, we determine the forbidden sets, introduce an explicit formula for the solutions and discuss the global behaviors of solutions of the difference equations $$\begin{array}{} \displaystyle x_{n+1}=\frac{ax_{n}x_{n-1}}{bx_{n-1}+ cx_{n-2}},\quad n=0,1,\ldots \end{array} $$ where a,b,c are positive real numbers and the initial conditions x−2,x−1,x0 are real numbers.