scholarly journals Global asymptotic behavior of solutions of a forced delay difference equation

2004 ◽  
Vol 47 (8-9) ◽  
pp. 1211-1224 ◽  
Author(s):  
Yuji Liu ◽  
Weigao Ge
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Delay Difference Equation ◽  
Delay Difference

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.

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 Oscillation of third-order delay difference equations with negative damping term

2018 ◽  
Vol 72 (1) ◽  
pp. 19
Author(s):  
Martin Bohner ◽  
Srinivasan Geetha ◽  
Srinivasan Selvarangam ◽  
Ethiraju Thandapani
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Comparison Theorems ◽  
Asymptotic Behavior Of Solutions ◽  
Delay Difference Equation ◽  
Third Order ◽  
Negative Damping ◽  
The Difference ◽  
Delay Difference Equations ◽  
Delay Difference

The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.<br /><br />

scholarly journals A new view on one problem of asymptotic behavior of solutions of delay difference equations

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
L. Shaikhet
Keyword(s):  
Asymptotic Behavior ◽  
Characteristic Equation ◽  
Stability Criterion ◽  
Positive Root ◽  
Asymptotic Behavior Of Solutions ◽  
Delay Difference Equation ◽  
Complex Roots ◽  
Linear Delay ◽  
Delay Difference Equations ◽  
Delay Difference

One known theorem on the asymptotic behavior of solution of linear delay difference equation is considered where a stability criterion is derived via a positive root of the corresponding characteristic equation. Two new directions for further investigation are proposed. The first direction is connected with a weakening of the known stability criterion; the second one is connected with consideration of negative and complex roots of the characteristic equation. A lot of pictures with stability regions and trajectories of considered processes are presented for visual demonstration of the proposed directions.

scholarly journals Asymptotic behavior of third order delay difference equations with a negative middle term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
S. Selvarangam ◽  
S. Geetha ◽  
E. Thandapani ◽  
J. Alzabut
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Sufficient Conditions ◽  
Delay Difference Equation ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Middle Term ◽  
The Third ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractIn this paper, we establish some sufficient conditions which ensure that the solutions of the third order delay difference equation with a negative middle term $$ \Delta \bigl(a_{n}\Delta (\Delta w_{n})^{\alpha } \bigr)-p_{n}(\Delta w_{n+1})^{ \alpha }-q_{n}h(w_{n-l})=0,\quad n\geq n_{0}, $$ Δ ( a n Δ ( Δ w n ) α ) − p n ( Δ w n + 1 ) α − q n h ( w n − l ) = 0 , n ≥ n 0 , are oscillatory. Moreover, we study the asymptotic behavior of the nonoscillatory solutions. Two illustrative examples are included for illustration.

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