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
2004 ◽  
Vol 11 (1) ◽  
pp. 177-185
Author(s):  
Xian Hua Tang ◽  
Sui Sun Cheng

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.


1999 ◽  
Vol 30 (1) ◽  
pp. 39-46
Author(s):  
WAN-TONG LI ◽  
SUI-SUN CHENG

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


1994 ◽  
Vol 25 (3) ◽  
pp. 257-265
Author(s):  
J. H. SHEN ◽  
Z. C. WANG ◽  
X. Z. QIAN

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 $c =1$.


2012 ◽  
Vol 14 (3) ◽  
pp. 432-444
Author(s):  
G. E. Chatzarakis ◽  
G. L. Karakostas ◽  
I. P. Stavroulakis

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Bin Qin ◽  
Hui Wu

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.


2009 ◽  
Vol 3 (8) ◽  
Author(s):  
Xiaohui Gong ◽  
Xiaozhu Zhong ◽  
Jianqiang Jia ◽  
Rui Ouyang ◽  
Hongqiang Han

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