scholarly journals Complete Characterizations of an Oscillatory Neutral Difference Equation

1998 ◽  
Vol 221 (1) ◽  
pp. 73-91 ◽  
Author(s):  
Sui Sun Cheng ◽  
Yi-Zhong Lin
Keyword(s):  
Difference Equation ◽  
Neutral Difference Equation

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 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

scholarly journals Convergence and Divergence of the Solutions of a Neutral Difference Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
G. E. Chatzarakis ◽  
G. N. Miliaras
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Difference Operator ◽  
Neutral Type ◽  
Retarded Argument ◽  
Real Numbers ◽  
Positive Real ◽  
Neutral Difference Equation ◽  
Forward Difference ◽  
Deviated Argument

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 .

scholarly journals A Comparison Theorem for Oscillation of the Even-Order Nonlinear Neutral Difference Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Quanxin Zhang
Keyword(s):  
Difference Equation ◽  
Comparison Theorem ◽  
Difference Equations ◽  
Neutral Delay ◽  
Neutral Difference Equation ◽  
Oscillation Criteria ◽  
Even Order ◽  
Delay Difference Equations ◽  
Delay Difference

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.

scholarly journals Oscillation theorems for second order difference equations woth negative neutral term

2015 ◽  
Vol 46 (4) ◽  
pp. 441-451 ◽  
Author(s):  
Ethiraju Thandapani ◽  
Devarajulu Seghar ◽  
Sandra Pinelas
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Second Order ◽  
Neutral Difference Equation ◽  
Order Difference ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Oscillation Theorems ◽  
Positive Integers

In this paper we obtain some new oscillation criteria for the neutral difference equation \begin{equation*} \Delta \Big(a_n (\Delta (x_n-p_n x_{n-k}))\Big)+q_n f(x_{n-l})=0 \end{equation*} where $0\leq p_n\leq p0$ and $l$ and $k$ are positive integers. Examples are presented to illustrate the main results. The results obtained in this paper improve and complement to the existing results.

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