On the solutions of a second order difference equation

Abstract

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.

On the Boundedness solutions of the difference equation xn+1=axan+bxan-1, 0< a ≤ 2 and its application in medicine

“…For the periodicity of our dynamic for α = 2 it is already discussed in [R. Abo-Zeid (2017)],The dynamics is two period solution…”

“…• 2) All solutions of (3) converge to zero if and only if max{λ 1 , λ 2 , } < 1 For boundedness solutions of (3) one can refer to [R. Abo-Zeid (2017)] .Now for α = 2 which it is the aim of this paper we are ready to do some analysis and discussion about the global behavior of solutions of this difference equation:…”

“…In [R. Abo-Zeid (2017)] .R. Abo Zeid has discussed the global behavior of all solutions of the difference equation:…”

Global behavior of a third order difference equation with quadratic term

“…Recently, there has been a great interest in studying properties of nonlinear and rational difference equations (see [1,[4][5][6][7][8][9][10] and the references therein).…”

Behavior of solutions of a second order rational difference equation

“…They conjectured that the unique positive equilibrium point is globally asymptotically stable and confirmed it only when (α − c) 2 ≤ 4. Kulenović et al [24], studied equation (1) and gave a unified proof for all values of α that the unique equilibrium is globally asymptotically stable. For more on difference equations with quadratic terms, see [1]- [14], [16], [17], [19], [21]- [25], [27]- [29].…”