scholarly journals On oscillation of second-order noncanonical neutral differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Muhib
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

AbstractIn the present work, we study the second-order neutral differential equation and formulate new oscillation criteria for this equation. Our conditions differ from the earlier ones. Also, our results are expansions and generalizations of some previous results. Examples to illustrate the main results are included.

Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Chenghui Zhang ◽  
Blanka Baculíková ◽  
Jozef Džurina ◽  
Tongxing Li
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
All Solutions

AbstractWe obtain some oscillation criteria for all solutions to a second-order mixed neutral differential equation with distributed deviating arguments. The results presented improve those reported in the literature.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments

2017 ◽  
Vol 67 (3) ◽  
Author(s):  
Simona Fišnarová ◽  
Robert Mařík
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Linear Differential

AbstractIn this paper we derive oscillation criteria for the second order half-linear neutral differential equationwhere Φ(

scholarly journals Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Osama Moaaz ◽  
Ali Muhib ◽  
Saud Owyed ◽  
Emad E. Mahmoud ◽  
Aml Abdelnaser
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
New Criteria ◽  
Oscillation Of Solutions

The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation r l u ′ l γ ′ + q l x β σ l = 0 , where l ≥ l 0 and u l ≔ x l + p x ϱ l . By optimizing the commonly used relationship x > 1 − p u , we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.

scholarly journals On Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Damped Neutral Differential Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Ercan Tunç ◽  
Said R. Grace
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations

This paper discusses oscillatory and asymptotic properties of solutions of a class of second-order nonlinear damped neutral differential equations. Some new sufficient conditions for any solution of the equation to be oscillatory or to converge to zero are given. The results obtained extend and improve some of the related results reported in the literature. The results are illustrated with examples.

scholarly journals New Oscillation Results for Second-Order Neutral Differential Equations with Deviating Arguments

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1937
Author(s):  
Yakun Wang ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Delay Differential ◽  
The Right

In this paper, we focus on the second-order neutral differential equations with deviating arguments which are under the canonical condition. New oscillation criteria are established, which are based on a first-order delay differential equation and generalized Riccati transformations. The idea of symmetry is a useful tool, not only guiding us in the right way to study this function but also simplifies our proof. Our results are generalizations of some previous results and we provide an example to illustrate the main results.

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.

scholarly journals Oscillation Conditions for Certain Fourth-Order Non-Linear Neutral Differential Equation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1096 ◽  
Author(s):  
Ioannis Dassios ◽  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Neutral Differential Equation ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Non Linear ◽  
The Right ◽  
Oscillation Of Solutions

In this work, new conditions were obtained for the oscillation of solutions of fourth-order non-linear neutral differential equations (NDEs) using the Riccati technique. These oscillation criteria complement and improve those of Chatzarakis et al. (2019). Symmetry plays an important role in determining the right way to study these equation. An example is given to illustrate our theory.

scholarly journals Oscillation of higher-order half-linear neutral differential equations

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Shuhong Tang ◽  
Tongxing Li ◽  
E. Thandapani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Higher Order ◽  
Neutral Differential Equation ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

AbstractIn this paper, we establish some new oscillation criteria for the higher-order half-linear neutral differential equation

scholarly journals Oscillation of second order neutral differential equations

1989 ◽  
Vol 39 (1) ◽  
pp. 71-80 ◽  
Author(s):  
L.H. Erbe ◽  
B.G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Image Position

Some new sufficient conditions are obtained for the oscillation of the neutral differential equationwhere r(t) > 0, 0 < c < 1, p(t) ≥ 0, σ(t) > τ > 0 and α = 1 or 0 < α < 1.

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