scholarly journals Asymptotic Behavior of a Forced Difference Equation

1996 ◽  
Vol 203 (2) ◽  
pp. 388-400 ◽  
Author(s):  
J.R. Graef ◽  
C. Qian
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation

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 .

Global asymptotic behavior of a two-dimensional difference equation modelling competition

2003 ◽  
Vol 52 (7) ◽  
pp. 1765-1776 ◽  
Author(s):  
Dean Clark ◽  
M.R.S. Kulenović ◽  
James F. Selgrade
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Two Dimensional ◽  
Equation Modelling

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.

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