On the recursive sequence xn+1=A∏i=lkxn−2i−1B+C∏i=lk−1xn−2i
Alaa E. Hamza,R. Khalaf-Allah +1 more
TLDR
This work investigates the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation and discusses the existence of unbounded solutions under certain conditions when l = 0.Abstract:
The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation x n + 1 = A ∏ i = l k x n − 2 i − 1 B + C ∏ i = l k − 1 x n − 2 i , n = 0 , 1 , … where A , B , C are nonnegative real numbers and l , k are nonnegative integers, l k . We discuss the existence of unbounded solutions under certain conditions when l = 0 .read more
Citations
More filters
Journal ArticleDOI
On positive solutions of a (k+1)th order difference equation
TL;DR: It is shown that the following difference equation, x n + 1, has a positive solution which converges to zero and solves Open Problem 11.4.10.
Journal ArticleDOI
On the difference equation xn = xn−2/(bn + cnxn−1xn−2)
TL;DR: It is proved that the difference equation x n, where x n is sequences periodic with period two and the initial values x −2, x −1 are real numbers, can be solved explicitly.
Journal ArticleDOI
Solution and Attractivity for a Rational Recursive Sequence
TL;DR: In this paper, the behavior of solution of the nonlinear difference equation is studied and shown to be similar to the one in the present paper; see Section 2.2.1.
Journal ArticleDOI
Asymptotics of Some Classes of Higher-Order Difference Equations
TL;DR: In this paper, the authors present methods for finding asymptotics of some classes of nonlinear higher-order difference equations, and confirm a conjecture posed by S. Stevic (2005).
Journal ArticleDOI
Global behaviours of rational difference equations of orders two and three with quadratic terms
TL;DR: In this article, the authors determine the global behaviors of all solutions of the following rational difference equations via semiconjugate relations that also let them reduce them to first-order equations, and show that for initial values outside the forbidden sets, their solutions may converge to 0, or to a positive fixed point, or they may be periodic of period 2 or unbounded.
References
More filters
Book
Global Behavior of Nonlinear Difference Equations of Higher Order with Applications
V.L. Kocic,G. Ladas +1 more
TL;DR: The Riccati Difference Equation as discussed by the authors is a generalization of the generalized contraction principle for nonlinear difference equations. But it is not suitable for systems of nonlinear change equations.
Book
Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures
Mustafa R. S. Kulenović,G. Ladas +1 more
TL;DR: The Riccati Equation Semicycle Analysis (RSESA) as discussed by the authors has been used to study the stability and linearized stability of the positive equilibrium in the zero equilibrium.
Book ChapterDOI
Open problems and conjectures
V. L. Kocic,G. Ladas +1 more
TL;DR: The aim in this chapter is to present some conjectures and some open problems about some interesting types of difference equations.
Journal ArticleDOI
Global stability and asymptotics of some classes of rational difference equations
TL;DR: In this paper, the positive solutions of some classes of rational difference equations are globally asymptotically stable, using a Berg's result, and they also find the positive solution of some solutions of these equations.
Journal ArticleDOI
Global asymptotic stability for two recursive difference equations
Xianyi Li,Deming Zhu +1 more
TL;DR: Two sufficient conditions are obtained for the global asymptotic stability of the following two recursive difference equations.
Related Papers (5)
On the recursive sequence x n+1 =AΠ K i=l' x n -2 j -1 / B + C Π k-l i=l' x n -2 i
Alaa E. Hamza,R. Khalaf-Allah +1 more
The difference equation xn+1=α+xn−k∑i=0k−1cixn−i has solutions converging to zero
Global asymptotic stability of a higher order rational difference equation
Taixiang Sun,Hongjian Xi +1 more