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 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 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 of Third-Order Nonlinear Damped Dynamic Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yang-Cong Qiu
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Oscillation Criteria ◽  
Function Classes ◽  
Generalized Riccati Transformation

We establish oscillation criteria of third-order nonlinear damped dynamic equations on time scales of the formr1tr2txΔtγΔΔ+ft, xt,xσt, xgt, xΔt=0by employing functions in some function classes and the generalized Riccati transformation. Two examples are given to show the significance of the conclusions.

scholarly journals Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yakun Wang ◽  
Fanwei Meng ◽  
Juan Gu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation

AbstractOur objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example 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.

scholarly journals Oscillation criteria of certain fractional partial differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Di Xu ◽  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Riccati Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

Abstract In this article, we regard the generalized Riccati transformation and Riemann–Liouville fractional derivatives as the principal instrument. In the proof, we take advantage of the fractional derivatives technique with the addition of interval segmentation techniques, which enlarge the manners to demonstrate the sufficient conditions for oscillation criteria of certain fractional partial differential equations.

scholarly journals New Oscillatory Behavior of Third-Order Nonlinear Delay Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Li Gao ◽  
Quanxin Zhang ◽  
Shouhua Liu
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Generalized Riccati Transformation ◽  
Delay Dynamic Equations ◽  
Inequality Technique ◽  
Nonlinear Delay

A class of third-order nonlinear delay dynamic equations on time scales is studied. By using the generalized Riccati transformation and the inequality technique, four new sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially improve earlier ones. Some examples are considered to illustrate the main results.

scholarly journals On the Oscillation of Even-Order Half-Linear Functional Difference Equations with Damping Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yaşar Bolat ◽  
Jehad Alzabut
Keyword(s):  
Real Number ◽  
Difference Equations ◽  
Linear Functional ◽  
Oscillatory Behavior ◽  
Functional Difference ◽  
Riccati Transformation ◽  
Damping Term ◽  
Generalized Riccati Transformation ◽  
Even Order ◽  
Functional Difference Equations

We investigate the oscillatory behavior of solutions of themth order half-linear functional difference equations with damping term of the formΔ[pnQ(Δm-1yn)]+qnQ(Δm-1yn)+rnQ(yτn)=0,n≥n0, wheremis even andQ(s)=sα-2s,α>1is a fixed real number. Our main results are obtained via employing the generalized Riccati transformation. We provide two examples to illustrate the effectiveness of the proposed results.

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 Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
M. Tamer Şenel
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Transformation ◽  
Type Oscillation

The oscillation of solutions of the second-order nonlinear dynamic equation(r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t))γ+f(t,x(g(t)))=0, with damping on an arbitrary time scaleT, is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.

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