scholarly journals GLOBAL ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR EXPONENTIAL FORM DIFFERENCE EQUATIONS WITH THREE PARAMETERS

2016 ◽  
Vol 6 (3) ◽  
pp. 600-606
Author(s):  
Hui Feng ◽  
◽  
Huili Ma ◽  
Wandi Ding ◽  
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Exponential Form

On some difference equations of exponential form

2018 ◽  
pp. 581-584
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
Real Numbers ◽  
Positive Real ◽  
Exponential Form ◽  
Numerical Examples

In this paper, the local asymptotic behavior of positive solutions of some exponential difference equations x_(n+1)=(x_n+x_(n-k))/(1+x_(n-k) e^(x_(n-k) ) ) , k ∈ N, n=0,1,2,… are investigated where the initial conditions are arbitrary positive real numbers. Furthermore, some numerical examples are presented to verify our results.

scholarly journals Asymptotic Behavior of the Solutions of System of Difference Equations of Exponential Form

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Vu Van Khuong ◽  
Tran Hong Thai
Keyword(s):  
Asymptotic Behavior ◽  
Rate Of Convergence ◽  
Positive Solutions ◽  
Difference Equations ◽  
System Of Difference Equations ◽  
Positive Real ◽  
Exponential Form ◽  
Initial Values

The goal of this paper is to study the boundedness, the persistence, and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form: xn+1=a+be-yn+ce-xn/d+hyn, yn+1=a+be-xn+ce-yn/d+hxn, where a, b, c, d, and h are positive constants and the initial values x0, y0 are positive real values. Also, we determine the rate of convergence of a solution that converges to the equilibrium E=(x-,y-) of this system.

Long-term behavior of positive solutions of an exponentially self-regulating system of difference equations

2017 ◽  
Vol 10 (03) ◽  
pp. 1750045 ◽  
Author(s):  
N. Psarros ◽  
G. Papaschinopoulos ◽  
K. B. Papadopoulos
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
System Of Difference Equations ◽  
Long Term Behavior

In this paper, we study the asymptotic behavior of the positive solutions of a system of the following difference equations: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are positive constants and the initial conditions [Formula: see text] and [Formula: see text] are positive numbers.

scholarly journals On the system of two nonlinear difference equationsxn+1=A+xn−1/yn,   yn+1=A+yn−1/xn

2000 ◽  
Vol 23 (12) ◽  
pp. 839-848 ◽  
Author(s):  
G. Papaschinopoulos ◽  
C. J. Schinas
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Positive Constant ◽  
Oscillatory Behavior ◽  
Nonlinear Difference Equations

We study the oscillatory behavior, the periodicity and the asymptotic behavior of the positive solutions of the system of two nonlinear difference equationsxn+1=A+xn−1/ynandyn+1=A+yn−1/xn, whereAis a positive constant, andn=0,1,….

scholarly journals Asymptotic Behavior of Solutions to Half-Linearq-Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Pavel Řehák
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Special Limit ◽  
Bounded Functions ◽  
Necessary And Sufficient

We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linearq-difference equationDq(Φ(Dqy(t)))+p(t)Φ(y(qt))=0,t∈{qk:k∈N0}withq>1,Φ(u)=|u|α−1sgn⁡uwithα>1, to behave likeq-regularly varying orq-rapidly varying orq-regularly bounded functions (that is, the functionsy, for which a special limit behavior ofy(qt)/y(t)ast→∞is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.

Existence of Positive Solutions for a Class of Higher-Order Neutral Delay Difference Equations

2011 ◽  
Vol 50-51 ◽  
pp. 761-765
Author(s):  
Dong Hua Wang ◽  
Yu Huan Cui ◽  
Pu Yu Hao
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Higher Order ◽  
Sufficient Condition ◽  
Neutral Delay ◽  
Existence Of Positive Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

In this paper, a class of higher-order neutral delay difference equations is investigated. Some sufficient condition of the asymptotic behavior and existence of positive solutions for the equations are obtained. At last, we give their applications to some more general equations.

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