scholarly journals Existence of a nonoscillatory solution of a second-order linear neutral difference equation

2007 ◽  
Vol 20 (8) ◽  
pp. 892-899 ◽  
Author(s):  
Jinfa Cheng
Keyword(s):  
Difference Equation ◽  
Nonoscillatory Solution ◽  
Second Order ◽  
Neutral Difference Equation ◽  
Order Linear

scholarly journals Existence of Nonoscillatory Solution of High Order Linear Neutral Delay Difference Equation

2008 ◽  
Vol 2 (6) ◽  
Author(s):  
Shasha Zhang ◽  
Xiaozhu Zhong ◽  
Ping Yu ◽  
Wenxia Zhang ◽  
Ning Li
Keyword(s):  
Difference Equation ◽  
Nonoscillatory Solution ◽  
High Order ◽  
Delay Difference Equation ◽  
Neutral Delay ◽  
Order Linear ◽  
Delay Difference

scholarly journals Conjugacy and phases for second order linear difference equation

2007 ◽  
Vol 53 (7) ◽  
pp. 1129-1139 ◽  
Author(s):  
Zuzana Došlá ◽  
Šárka Pechancová
Keyword(s):  
Difference Equation ◽  
Linear Difference Equation ◽  
Second Order ◽  
Order Linear

Fibonacci and Lucas polynomials

1981 ◽  
Vol 90 (3) ◽  
pp. 385-387 ◽  
Author(s):  
B. G. S. Doman ◽  
J. K. Williams
Keyword(s):  
Difference Equation ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Linear Difference Equation ◽  
Second Order ◽  
Lucas Numbers ◽  
Order Linear ◽  
Lucas Polynomials ◽  
Fibonacci And Lucas Numbers

The Fibonacci and Lucas polynomials Fn(z) and Ln(z) are denned. These reduce to the familiar Fibonacci and Lucas numbers when z = 1. The polynomials are shown to satisfy a second order linear difference equation. Generating functions are derived, and also various simple identities, and relations with hypergeometric functions, Gegenbauer and Chebyshev polynomials.

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.

scholarly journals OSCILLATION CRITERIA FOR SECOND ORDER LINEAR GENERALIZED DIFFERENCE EQUATION

2017 ◽  
Vol 114 (3) ◽  
Author(s):  
M.M.S. Manuel ◽  
P.V.M. Reddy
Keyword(s):  
Difference Equation ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Linear

scholarly journals Existence of Nonoscillatory Solution of Second Order Linear Neutral Delay Equation

1998 ◽  
Vol 228 (2) ◽  
pp. 436-448 ◽  
Author(s):  
M.R.S. Kulenović ◽  
S. Hadžiomerspahić
Keyword(s):  
Nonoscillatory Solution ◽  
Second Order ◽  
Delay Equation ◽  
Neutral Delay ◽  
Order Linear

scholarly journals Instability of second-order nonhomogeneous linear difference equations with real-valued coefficients

2021 ◽  
Vol 37 (3) ◽  
pp. 489-495
Author(s):  
MASAKAZU ONITSUKA ◽  
◽  
Keyword(s):  
Difference Equation ◽  
Linear Difference Equation ◽  
Second Order ◽  
Ulam Stability ◽  
Necessary And Sufficient Condition ◽  
Linear Difference Equations ◽  
Real Numbers ◽  
Step Size ◽  
Order Linear ◽  
Necessary And Sufficient

In J. Comput. Anal. Appl. (2020), pp. 152--165, the author dealt with Hyers--Ulam stability of the second-order linear difference equation $\Delta_h^2x(t)+\alpha \Delta_hx(t)+\beta x(t) = f(t)$ on $h\mathbb{Z}$, where $\Delta_hx(t) = (x(t+h)-x(t))/h$ and $h\mathbb{Z} = \{hk|\,k\in\mathbb{Z}\}$ for the step size $h>0$; $\alpha$ and $\beta$ are real numbers; $f(t)$ is a real-valued function on $h\mathbb{Z}$. The purpose of this paper is to clarify that the second-order linear difference equation has no Hyers--Ulam stability when the step size $h>0$ and the coefficients $\alpha$ and $\beta$ satisfy suitable conditions. Finally, a necessary and sufficient condition for Hyers--Ulam stability is obtained.

Remarks on oscillation of second-order linear difference equation

2009 ◽  
Vol 215 (8) ◽  
pp. 2855-2857 ◽  
Author(s):  
Caiming Lei
Keyword(s):  
Difference Equation ◽  
Linear Difference Equation ◽  
Second Order ◽  
Order Linear
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