Boundedness and global stability of a higher-order difference equation

2008 ◽  
Vol 14 (10-11) ◽  
pp. 1035-1044 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Higher Order ◽  
Order Difference ◽  
Order Difference Equation

Global behavior of a higher order difference equation

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
R. Abo-Zeid
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Positive Solutions ◽  
Higher Order ◽  
Global Behavior ◽  
Real Numbers ◽  
Order Difference ◽  
Order Difference Equation ◽  
The Difference

AbstractThe aim of this paper is to investigate the global stability and periodic nature of the positive solutions of the difference equation $$x_{n + 1} = \frac{{A + Bx_{n - 2k - 1} }} {{C + D\prod\limits_{i = 1}^k {x_{n - 2i} } }}, n = 0,1,2, \ldots ,$$ where A, B are nonnegative real numbers, C,D > 0 and l, k are nonnegative integers such that l ≤ k.

scholarly journals Global Attractivity of a Higher-Order Difference Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
R. Abo-Zeid
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Global Attractivity ◽  
Higher Order ◽  
Real Numbers ◽  
Positive Real ◽  
Order Difference ◽  
Order Difference Equation ◽  
Admissible Solutions ◽  
The Difference

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.

scholarly journals Multiplicity of Periodic Solutions for a Higher Order Difference Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ronghui Hu
Keyword(s):  
Difference Equation ◽  
Periodic Solutions ◽  
Higher Order ◽  
Critical Groups ◽  
Order Difference ◽  
Reduction Methods ◽  
Order Difference Equation

We study a higher order difference equation. By Lyapunov-Schmidt reduction methods and computations of critical groups, we prove that the equation has fourM-periodic solutions.

Periodicity of the solution of a higher order difference equation

2018 ◽  
Author(s):  
A. M. Alotaibi ◽  
M. S. M. Noorani ◽  
M. A. El-Moneam
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Order Difference ◽  
Order Difference Equation
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