Non-Oscillatory Solutions of Higher Order Nonlinear Neutral Delay Difference Equation

2003 ◽  
pp. 959-975
Author(s):  
YONG ZHOU
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Oscillatory Solutions ◽  
Delay Difference

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.

Oscillatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations

1996 ◽  
Vol 38 (2) ◽  
pp. 163-171 ◽  
Author(s):  
John R. Graef ◽  
Agnes Miciano ◽  
Paul W. Spikes ◽  
P. Sundaram ◽  
E. Thandapani
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Difference Equations ◽  
Neutral Type ◽  
Higher Order ◽  
Asymptotic Behavior Of Solutions ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Image Position ◽  
Delay Difference

AbstractThe authors consider the higher-order nonlinear neutral delay difference equationand obtain results on the asymptotic behavior of solutions when (pn) is allowed to oscillate about the bifurcation value –1. We also consider the case where the sequence {pn} has arbitrarily large zeros. Examples illustrating the results are included, and suggestions for further research are indicated.

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