scholarly journals Qualitative Property of Third-Order Nonlinear Neutral Distributed-Delay Generalized Difference Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
M. Sumathy ◽  
P. Venkata Mohan Reddy ◽  
M. Maria Susai Manuel
Keyword(s):  
Difference Equations ◽  
Distributed Delay ◽  
Qualitative Property ◽  
Riccati Transformation ◽  
Third Order ◽  
Oscillation Criteria

This paper investigates the qualitative property of third-order nonlinear neutral distributed-delay generalized difference equations. By utilizing Philos-type technique and Riccati transformation, some oscillation criteria are presented to ensure that every solution of this equation oscillates or converges to zero. To illustrate the significance of our main result, we provide a suitable example.

scholarly journals Oscillation Criteria for Third Order Neutral Generalized Difference Equations with Distributed Delay

2019 ◽  
Author(s):  
P.Venkata Mohan Reddy ◽  
M.Maria Susai Manuel ◽  
Adem Kilicman
Keyword(s):  
Difference Equations ◽  
Distributed Delay ◽  
Oscillatory Solution ◽  
Riccati Transformation ◽  
Third Order ◽  
Type Method ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

This paper aims to investigate the criteria of behaviour of certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, some oscillation criteria are obtained to ensure convergence and oscillatory solution of suitable example is listed to illustrate the main result.

scholarly journals Oscillation Criteria for Third Order Neutral Generalized Difference Equations with Distributed Delay

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1501
Author(s):  
P. Venkata Mohan Reddy ◽  
M. Maria Susai Manuel ◽  
Adem Kılıçman
Keyword(s):  
Difference Equations ◽  
Distributed Delay ◽  
Riccati Transformation ◽  
Third Order ◽  
Oscillatory Solutions ◽  
Type Method ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

This paper aims to investigate the criteria of behavior of a certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, we obtain criteria to ensure convergence and oscillatory solutions and suitable examples are provided to illustrate the main results.

scholarly journals Oscillation of nonlinear third-order difference equations with mixed neutral terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jehad Alzabut ◽  
Martin Bohner ◽  
Said R. Grace
Keyword(s):  
Difference Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Order Difference ◽  
New Approach ◽  
Comparison Technique

AbstractIn this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

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.

scholarly journals Oscillation criteria for certain third order nonlinear difference equations

2009 ◽  
Vol 3 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Said Grace ◽  
Ravi Agarwal ◽  
John Graef
Keyword(s):  
Difference Equations ◽  
Nonlinear Difference Equations ◽  
Third Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
New Criteria

Some new criteria for the oscillation of all solutions of third order nonlinear difference equations of the form ? (a(n)(?2 x(n))? + q(n)f (x[g(n)]) = 0 and ? (a(n)(?2 x(n))? = q(n)f (x[g(n)]) + p(n)h(x[?(n)]) ? -1/? with P a (n) < ? are established.

scholarly journals Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 86
Author(s):  
Yang-Cong Qiu ◽  
Kuo-Shou Chiu ◽  
Said R. Grace ◽  
Qingmin Liu ◽  
Irena Jadlovská
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Neutral Dynamic Equations ◽  
Oscillation Of Solutions

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

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.

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