MODIFIED OSCILLATION CRITERIA OF SECOND-ORDER NEUTRAL DIFFERENCE EQUATIONS

2021 ◽  
Vol 28 (1-2) ◽  
pp. 19-30
Author(s):  
G. CHATZARAKIS G. CHATZARAKIS ◽  
R. KANAGASABAPATHI R. KANAGASABAPATHI ◽  
S. SELVARANGAM S. SELVARANGAM ◽  
E. THANDAPANI E. THANDAPANI
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Riccati Transformation ◽  
Nonlinear Difference Equations ◽  
Transformation Technique ◽  
Neutral Difference Equations ◽  
Oscillation Criteria ◽  
Neutral Term

In this paper we shall consider a class of second-order nonlinear difference equations with a negative neutral term. Some new oscillation criteria are obtained via Riccati transformation technique. These criteria improve and modify the existing results mentioned in the literature. Some examples are given to show the applicability and significance of the main results.

Oscillation Theorems of Nonlinear Difference Equations of Second Order

2003 ◽  
Vol 10 (2) ◽  
pp. 343-352
Author(s):  
S. H. Saker
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Riccati Transformation ◽  
Nonlinear Difference Equations ◽  
Transformation Techniques ◽  
Oscillation Criteria ◽  
Special Cases ◽  
Oscillation Theorems

Abstract Using the Riccati transformation techniques, we establish some new oscillation criteria for the second-order nonlinear difference equation Some comparison between our theorems and the previously known results in special cases are indicated. Some examples are given to illustrate the relevance of our results.

scholarly journals Oscillation Criteria for Second Order Impulsive Delay Dynamic Equations on Time Scale

2021 ◽  
Vol 45 (4) ◽  
pp. 531-542
Author(s):  
GOKULA NANDA CHHATRIA ◽  
Keyword(s):  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Impulsive Delay

In this work, we study the oscillation of a kind of second order impulsive delay dynamic equations on time scale by using impulsive inequality and Riccati transformation technique. Some examples are given to illustrate our main results.

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 of second-order nonlinear difference equations with sublinear neutral term

2019 ◽  
Vol 23 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Martin Bohner ◽  
Hassan El-Morshedy ◽  
Said Grace ◽  
Ilgin Sağer
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Neutral Term

scholarly journals Some Remark on Oscillation of Second Order Impulsive Delay Dynamic Equations on Time Scales

2020 ◽  
Vol 76 (1) ◽  
pp. 115-126
Author(s):  
Gokula Nanda Chhatria
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Second Order ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Impulsive Delay

AbstractThis article deals with the oscillation criteria for a very extensively studied second order impulsive delay dynamic equations on time scale by using the Riccati transformation technique. Some examples are given to show the effect of impulse and to illustrate our main results.

scholarly journals Oscillatory Behavior of Second Order Nonlinear Difference Equations with a Non-Positive Neutral Term

2018 ◽  
Vol 2(2018) (1) ◽  
pp. 240-252
Author(s):  
Said R. Grace ◽  
◽  
Shurong Sun ◽  
Limei Feng ◽  
Ying Sui ◽  
...  
Keyword(s):  
Difference Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Neutral Term
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