Asymptotic Constancy to the Neutral Delay Difference Equation

2017 ◽  
Author(s):  
Yoshihiro Hamaya
Keyword(s):  
Difference Equation ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Delay Difference ◽  
Asymptotic Constancy

Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δ m

2021 ◽  
Vol 71 (1) ◽  
pp. 129-146
Author(s):  
Chittaranjan Behera ◽  
Radhanath Rath ◽  
Prayag Prasad Mishra
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Variable Delays ◽  
All Solutions ◽  
Delay Difference

Abstract In this article we obtain sufficient conditions for the oscillation of all solutions of the higher-order delay difference equation Δ m ( y n − ∑ j = 1 k p n j y n − m j ) + v n G ( y σ ( n ) ) − u n H ( y α ( n ) ) = f n , $$\begin{array}{} \displaystyle \Delta^{m}\big(y_n-\sum_{j=1}^k p_n^j y_{n-m_j}\big) + v_nG(y_{\sigma(n)})-u_nH(y_{\alpha(n)})=f_n\,, \end{array}$$ where m is a positive integer and Δ xn = x n+1 − xn . Also we obtain necessary conditions for a particular case of the above equation. We illustrate our results with examples for which it seems no result in the literature can be applied.

scholarly journals Some Oscillation Results for Even Order Delay Difference Equations with a Sublinear Neutral Term

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Govindasamy Ayyappan ◽  
Gunasekaran Nithyakala
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Neutral Term ◽  
All Solutions ◽  
Even Order ◽  
Delay Difference Equations ◽  
Delay Difference

In this paper, some new results are obtained for the even order neutral delay difference equationΔanΔm-1xn+pnxn-kα+qnxn-lβ=0, wherem≥2is an even integer, which ensure that all solutions of the studied equation are oscillatory. Our results extend, include, and correct some of the existing results. Examples are provided to illustrate the importance of the main results.

scholarly journals Necessary and sufficient conditions for oscillation of first order neutral delay difference equations

2015 ◽  
Vol 3 (2) ◽  
pp. 61
Author(s):  
A. Murgesan ◽  
P. Sowmiya
Keyword(s):  
Difference Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
First Order ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
Delay Difference Equations ◽  
Delay Difference

<p>In this paper, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the first order neutral delay difference equation with constant coefficients of the form <br />\begin{equation*} \quad \quad \quad \quad \Delta[x(n)-px(n-\tau)]+qx(n-\sigma)=0, \quad \quad n\geq n_0 \quad \quad \quad \quad \quad \quad {(*)} \end{equation*}<br />by constructing several suitable auxiliary functions. Some examples are also given to illustrate our results.</p>

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