scholarly journals Oscillatory Properties of Odd-Order Delay Differential Equations with Distribution Deviating Arguments

2020 ◽  
Vol 10 (17) ◽  
pp. 5952
Author(s):  
Ali Muhib ◽  
Thabet Abdeljawad ◽  
Osama Moaaz ◽  
Elmetwally M. Elabbasy
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Comparison Theorems ◽  
Iterative Technique ◽  
Deviating Arguments ◽  
First Order ◽  
Odd Order ◽  
All Solutions ◽  
Delay Differential ◽  
New Criteria

Throughout this work, new criteria for the asymptotic behavior and oscillation of a class of odd-order delay differential equations with distributed deviating arguments are established. Our method is essentially based on establishing sharper estimates for positive solutions of the studied equation, using an iterative technique. Moreover, the iterative technique allows us to test the oscillation, even when the related results fail to apply. By establishing new comparison theorems that compare the nth-order equations with one or a couple of first-order delay differential equations, we obtain new conditions for oscillation of all solutions of the studied equation. To show the importance of our results, we provide two examples.

scholarly journals COMPARISON THEOREMS ON THE OSCILLATION AND ASYMPTOTIC BEHAVIOUR OF HIGHER-ORDER NEUTRAL DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 52 (1) ◽  
pp. 107-114 ◽  
Author(s):  
BAŞAK KARPUZ ◽  
ÖZKAN ÖCALAN ◽  
SERMIN ÖZTÜRK
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Delay Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Delay Differential ◽  
Asymptotic Behaviours

AbstractIn this work, oscillatory and asymptotic behaviours of all solutions of higher-order neutral differential equations are compared with first-order delay differential equations, depending on two different ranges of the coefficient associated with the neutral part. Some simple examples are given to compare our results with the existing results in the literature and to illustrate the significance and applicability of our new results. Our results generalise, improve and correct some of the existing results in the literature.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

scholarly journals Oscillation of Nonlinear First Order Neutral Differential Equations

2007 ◽  
Vol 4 (3) ◽  
pp. 485-490
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Integral Conditions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

scholarly journals Third-Order Neutral Delay Differential Equations: New Iterative Criteria for Oscillation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Osama Moaaz ◽  
Emad E. Mahmoud ◽  
Wedad R. Alharbi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Iterative Technique ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criterion ◽  
New Criteria

This study is aimed at developing new criteria of the iterative nature to test the oscillation of neutral delay differential equations of third order. First, we obtain a new criterion for the nonexistence of the so-called Kneser solutions, using an iterative technique. Further, we use several methods to obtain different criteria, so that a larger area of the models can be covered. The examples provided strongly support the importance of the new results.

scholarly journals Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Some new sufficient conditions for oscillation of all solutions of the first-order linear neutral delay differential equations are obtained. Our new results improve many well-known results in the literature. Some examples are inserted to illustrate our results.

scholarly journals Odd-order differential equations with deviating arguments: asymptomatic behavior and oscillation

2021 ◽  
Vol 19 (2) ◽  
pp. 1411-1425
Author(s):  
A. Muhib ◽  
◽  
I. Dassios ◽  
D. Baleanu ◽  
S. S. Santra ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Deviating Arguments ◽  
Odd Order ◽  
Even Order ◽  
Delay Differential

<abstract><p>Despite the growing interest in studying the oscillatory behavior of delay differential equations of even-order, odd-order equations have received less attention. In this work, we are interested in studying the oscillatory behavior of two classes of odd-order equations with deviating arguments. We get more than one criterion to check the oscillation in different methods. Our results are an extension and complement to some results published in the literature.</p></abstract>

scholarly journals Oscillations of First Order Linear Delay Differential Equations with positive and negative coefficients

2011 ◽  
Vol 8 (3) ◽  
pp. 806-809
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

Oscillation criteria are obtained for all solutions of the first-order linear delay differential equations with positive and negative coefficients where we established some sufficient conditions so that every solution of (1.1) oscillate. This paper generalized the results in [11]. Some examples are considered to illustrate our main results.

scholarly journals Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1177 ◽  
Author(s):  
George E. Chatzarakis ◽  
Jozef Džurina ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Differential Inequalities ◽  
Neutral Delay ◽  
Third Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria

In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations.

scholarly journals New Results for Kneser Solutions of Third-Order Nonlinear Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 686 ◽  
Author(s):  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Nonlinear Equation ◽  
Delay Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria ◽  
Nonlinear Delay

In this paper, we consider a certain class of third-order nonlinear delay differential equations r w ″ α ′ v + q v x β ς v = 0 , for v ≥ v 0 , where w v = x v + p v x ϑ v . We obtain new criteria for oscillation of all solutions of this nonlinear equation. Our results complement and improve some previous results in the literature. An example is considered to illustrate our main results.

scholarly journals Oscillatory behaviour of first order delay differential equations

1978 ◽  
Vol 19 (2) ◽  
pp. 183-190 ◽  
Author(s):  
Alexander Tomaras
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behaviour ◽  
First Order ◽  
All Solutions ◽  
Delay Differential

Best possible conditions are given here, under which all solutions of several delay differential equations are oscillatory.

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