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

Author(s):  
Xilan Liu ◽  
◽  
Dejie Deng ◽  
Huijuan Wang ◽  
◽  
...  
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].


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.


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 $c =1$.


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

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
G. E. Chatzarakis ◽  
G. N. Miliaras

We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form , where is a general retarded argument, is a general deviated argument (retarded or advanced), , is a sequence of positive real numbers such that , , and denotes the forward difference operator . Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to .


2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Quanxin Zhang

A comparison theorem on oscillation behavior is firstly established for a class of even-order nonlinear neutral delay difference equations. By using the obtained comparison theorem, two oscillation criteria are derived for the class of even-order nonlinear neutral delay difference equations. Two examples are given to show the effectiveness of the obtained results.


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