On the positive solutions of the difference equation system ,

2004 ◽  
Vol 158 (2) ◽  
pp. 303-305 ◽  
Author(s):  
Cengiz Çinar
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Equation System ◽  
The Difference

scholarly journals Global Behavior of the Difference Equationxn+1=xn-1g(xn)

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Bin Qin ◽  
Hui Wu
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Positive Solution ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Global Behavior ◽  
Initial Values ◽  
The Difference ◽  
Surjective Function

We consider the following difference equationxn+1=xn-1g(xn),n=0,1,…,where initial valuesx-1,x0∈[0,+∞)andg:[0,+∞)→(0,1]is a strictly decreasing continuous surjective function. We show the following. (1) Every positive solution of this equation converges toa,0,a,0,…,or0,a,0,a,…for somea∈[0,+∞). (2) Assumea∈(0,+∞). Then the set of initial conditions(x-1,x0)∈(0,+∞)×(0,+∞)such that the positive solutions of this equation converge toa,0,a,0,…,or0,a,0,a,…is a unique strictly increasing continuous function or an empty set.

scholarly journals On the Recursive Sequencexn+1=A+xnp/xn−1p

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Stevo Stevic
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Global Attractivity ◽  
Complete Picture ◽  
Boundedness Character ◽  
The Difference

This paper studies the boundedness, global attractivity, and periodicity of the positive solutions of the difference equationxn+1=A+xnp/xn−1p,n∈ℕ0, withp,A∈(0,∞). The main results give a complete picture regarding the boundedness character of the positive solutions of the equation.

scholarly journals On the Recursive Sequencexn=A+xn−kp/xn−1r

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Fangkuan Sun ◽  
Xiaofan Yang ◽  
Chunming Zhang
Keyword(s):  
Difference Equation ◽  
Dynamic Behavior ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Real Numbers ◽  
Positive Real ◽  
The Difference ◽  
The Stability

This paper studies the dynamic behavior of the positive solutions to the difference equationxn=A+xn−kp/xn−1r,n=1,2,…, whereA,p, andrare positive real numbers, and the initial conditions are arbitrary positive numbers. We establish some results regarding the stability and oscillation character of this equation forp∈(0,1).

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