scholarly journals Oscillation of third-order neutral differential equations with damping and distributed delay

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Meihua Wei ◽  
Cuimei Jiang ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Distributed Delay ◽  
Riccati Transformation ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
Integral Averaging Technique ◽  
Dynamic Inequality ◽  
Appl Math

Abstract The present paper focuses on the oscillation of the third-order nonlinear neutral differential equations with damping and distributed delay. The oscillation of the third-order damped equations is often discussed by reducing the equations to the second-order ones. However, by applying the Riccati transformation and the integral averaging technique, we give an analytical method for the estimation of Riccati dynamic inequality to establish several oscillation criteria for the discussed equation, which show that any solution either oscillates or converges to zero. The results make significant improvement and extend the earlier works such as (Zhang et al. in Appl. Math. Lett. 25:1514–1519 2012). Finally, some examples are given to demonstrate the effectiveness of the obtained oscillation results.

scholarly journals Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1021
Author(s):  
Marappan Sathish Kumar ◽  
Omar Bazighifan ◽  
Alanoud Almutairi ◽  
Dimplekumar N. Chalishajar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Riccati Transformation ◽  
Third Order ◽  
Transformation Techniques ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Type Oscillation

The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the integral averaging technique. The established criteria improve, simplify and complement results that have been published recently in the literature. An example is also given to demonstrate the applicability of the obtained conditions.

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 Boundedness and oscillation of third order neutral differential equations

2009 ◽  
Vol 43 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Božena Mihalíková ◽  
Eva Kostiková
Keyword(s):  
Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
The Relationship ◽  
Oscillation Of Solutions

Abstract The relationship between boundedness and oscillation of solutions of the third order neutral differential equations are presented.

scholarly journals Oscillatory Properties of Solutions of Even-Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 212 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Rami Ahmad El-Nabulsi ◽  
Osama Moaaz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Even Order ◽  
Oscillatory Properties

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using Riccati transformation and the integral averaging technique, we obtain a new oscillation criteria. This new theorem complements and improves some known results from the literature. An example is provided to illustrate the main results.

scholarly journals New Oscillation Criteria for Third-Order Nonlinear Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Quanxin Zhang ◽  
Li Gao ◽  
Shouhua Liu ◽  
Yuanhong Yu
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper discusses oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, three new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve the earlier ones.

scholarly journals Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order

2021 ◽  
Vol 5 (3) ◽  
pp. 95
Author(s):  
M. Sathish Kumar ◽  
R. Elayaraja ◽  
V. Ganesan ◽  
Omar Bazighifan ◽  
Khalifa Al-Shaqsi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Qualitative Behavior ◽  
Riccati Transformation ◽  
Third Order ◽  
Average Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Unbounded Solutions ◽  
Generalized Riccati Transformation ◽  
Integral Average

New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

scholarly journals Oscillation theorems for third order neutral differential equations

2012 ◽  
Vol 28 (2) ◽  
pp. 199-206
Author(s):  
BLANKA BACULIKOVA ◽  
◽  
J. DZURINA ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Order Equation ◽  
Comparison Theorems ◽  
Third Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
The Third ◽  
Oscillation Theorems

The aim of this paper is to study the asymptotic properties and the oscillation of the third order neutral differential equations ... Obtained results are based on the new comparison theorems, that permit to reduce the problem of the oscillation of the third order equation to the oscillation of the couple of the first order equation. Obtained comparison principles essentially simplify the examination of the studied equations.

Oscillation of certain third-order quasilinear neutral differential equations

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Linlin Yang ◽  
Zhiting Xu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Neutral Differential Equation ◽  
Third Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
The Third ◽  
Positive Integers ◽  
Type Oscillation

AbstractIn this paper, new oscillation criteria for the third-order quasilinear neutral differential equation $$\left( {a\left( t \right)\left( {z''\left( t \right)} \right)^\gamma } \right)^\prime + q\left( t \right)x^\gamma \left( {\tau \left( t \right)} \right) = 0, t \geqslant t_0 ,$$ are established, where z(t) = x(t) + p(t)x(δ(t)), and γ is a ratio of odd positive integers. Those results extend the oscillation criteria due to Sun [SUN, Y. G.: New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341–351] to the equation, and complement the existing results in literature. Two examples are provided to illustrate the relevance of our main theorems.

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