Comparison criteria of positive solutions for a neutral difference equation with positive and negative coefficients

1999 ◽  
Vol 15 (3) ◽  
pp. 326-332 ◽  
Author(s):  
Guan Xinping ◽  
Yu Yuanhong ◽  
Yang Jun
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Neutral Difference Equation ◽  
Positive And Negative Coefficients ◽  
Comparison Criteria

scholarly journals Positive Solutions of a Neutral Difference Equation with Positive and Negative Coefficients

2004 ◽  
Vol 11 (1) ◽  
pp. 177-185
Author(s):  
Xian Hua Tang ◽  
Sui Sun Cheng
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Neutral Difference Equation ◽  
Positive And Negative Coefficients ◽  
Positive Population

Abstract A neutral difference equation with positive and negative coefficients is a natural model for a population with depletion of the aged. In this paper, we obtain conditions which are sufficient for one such equation to support an eventually positive population.

scholarly journals AN OSCILLATiON THEOREM FOR A NEUTRAL DIFFERENCE EQUATION WITH POSITIVE AND NEGATIVE COEFFICIENTS

1999 ◽  
Vol 30 (1) ◽  
pp. 39-46
Author(s):  
WAN-TONG LI ◽  
SUI-SUN CHENG
Keyword(s):  
Difference Equation ◽  
Oscillation Criterion ◽  
Oscillation Theorem ◽  
Neutral Difference Equation ◽  
Positive And Negative Coefficients ◽  
Oscillation Theorems

An oscillation criterion is derived which supplements the oscillation theorems dervied in [1].

scholarly journals ON EXISTENCE OF POSITIVE SOLUTIONS OF NEUTRAL DIFFERENCE EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 257-265
Author(s):  
J. H. SHEN ◽  
Z. C. WANG ◽  
X. Z. QIAN
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Positive Solution ◽  
Positive Solutions ◽  
Difference Equations ◽  
Real Numbers ◽  
Neutral Difference Equation ◽  
Neutral Difference Equations ◽  
Existence Of Positive Solutions

Consider the neutral difference equation \[\Delta(x_n- cx_{n-m})+p_nx_{n-k}=0, n\ge N\qquad (*) \] where $c$ and $p_n$ are real numbers, $k$ and $N$ are nonnegative integers, and $m$ is positive integer. We show that if \[\sum_{n=N}^\infty |p_n|<\infty \qquad (**) \] then Eq.(*) has a positive solution when $c \neq 1$. However, an interesting example is also given which shows that (**) does not imply that (*) has a positive solution when $c =1$.

scholarly journals Convergence of the positive solutions of a nonlinear neutral difference equation

2012 ◽  
Vol 14 (3) ◽  
pp. 432-444
Author(s):  
G. E. Chatzarakis ◽  
G. L. Karakostas ◽  
I. P. Stavroulakis
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Neutral Difference Equation

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 Oscillation of First-order Neutral Difference Equation

2009 ◽  
Vol 3 (8) ◽  
Author(s):  
Xiaohui Gong ◽  
Xiaozhu Zhong ◽  
Jianqiang Jia ◽  
Rui Ouyang ◽  
Hongqiang Han
Keyword(s):  
Difference Equation ◽  
Neutral Difference Equation ◽  
First Order
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