scholarly journals Third-order neutral differential equations of the mixed type: Oscillatory and asymptotic behavior

2021 ◽  
Vol 19 (2) ◽  
pp. 1649-1658
Author(s):  
B. Qaraad ◽  
◽  
O. Moaaz ◽  
D. Baleanu ◽  
S. S. Santra ◽  
...  
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Differential Inequalities ◽  
Riccati Transformation ◽  
Third Order ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
New Criteria ◽  
Comparison Technique

<abstract><p>In this work, by using both the comparison technique with first-order differential inequalities and the Riccati transformation, we extend this development to a class of third-order neutral differential equations of the mixed type. We present new criteria for oscillation of all solutions, which improve and extend some existing ones in the literature. In addition, we provide an example to illustrate our results.</p></abstract>

scholarly journals New Oscillation Results for Third-Order Half-Linear Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 325 ◽  
Author(s):  
K. S. Vidhyaa ◽  
John R. Graef ◽  
E. Thandapani
Keyword(s):  
Differential Equations ◽  
Additional Result ◽  
Oscillation Theorem ◽  
Third Order ◽  
Transformation Technique ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Linear Delay ◽  
Delay Differential

The main purpose of this paper is to obtain criteria for the oscillation of all solutions of a third-order half-linear neutral differential equation. The main result in this paper is an oscillation theorem obtained by comparing the equation under investigation to two first order linear delay differential equations. An additional result is obtained by using a Riccati transformation technique. Examples are provided to show the importance of the 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 New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2177
Author(s):  
Saeed Althubiti ◽  
Ibtisam Aldawish ◽  
Jan Awrejcewicz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Essential Role ◽  
Differential Inequalities ◽  
Riccati Transformation ◽  
Neutral Differential Equations ◽  
First Order ◽  
Neutral Term ◽  
Even Order ◽  
Oscillation Of Solutions

The objective of this study is to establish new sufficient criteria for oscillation of solutions of even-order delay Emden-Fowler differential equations with neutral term rıyı+mıygın−1γ′+∑i=1jqiıyγμiı=0. We use Riccati transformation and the comparison with first-order differential inequalities to obtain theses criteria. Moreover, the presented oscillation conditions essentially simplify and extend known criteria in the literature. To show the importance of our results, we provide some examples. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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 Oscillatory and asymptotic properties of higher-order quasilinear neutral differential equations

2021 ◽  
Vol 6 (10) ◽  
pp. 11124-11138
Author(s):  
Clemente Cesarano ◽  
◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Ali Muhib ◽  
...  
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Higher Order ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Several Delays ◽  
New Criteria

<abstract><p>The objective of this paper is to study the oscillation criteria for odd-order neutral differential equations with several delays. We establish new oscillation criteria by using Riccati transformation. Our new criteria are interested in complementing and extending some results in the literature. An example is considered to illustrate our results.</p></abstract>

scholarly journals Oscillatory behavior of solutions of certain third order mixed neutral differential equations

2013 ◽  
Vol 44 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Ethiraj Thandapani ◽  
Renu Rama
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Positive Integers

The objective of this paper is to study the oscillatory and asymptotic properties of third order mixed neutral differential equation of the form $$ (a(t) [x(t) + b(t) x(t - \tau_{1}) + c(t) x(t + \tau_{2})]'')' + q(t) x^{\alpha}(t - \sigma_{1}) + p(t) x^{\beta}(t + \sigma_{2}) = 0 $$where $a(t), b(t), c(t), q(t)$ and $p(t)$ are positive continuous functions, $\alpha$ and $\beta$ are ratios of odd positive integers, $\tau_{1}, \tau_{2}, \sigma_{1}$ and $\sigma_{2}$ are positive constants. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converge to zero. Some examples are provided to illustrate the main results.

scholarly journals New criteria for oscillation of nonlinear neutral differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Delay Equations ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
First Order ◽  
Riccati Substitution ◽  
Gamma S ◽  
New Criteria

AbstractThe aim of this work is to offer sufficient conditions for the oscillation of neutral differential equation second order $$ \bigl( r ( t ) \bigl[ \bigl( y ( t ) +p ( t ) y \bigl( \tau ( t ) \bigr) \bigr) ^{\prime } \bigr] ^{\gamma } \bigr) ^{\prime }+f \bigl( t,y \bigl( \sigma ( t ) \bigr) \bigr) =0, $$(r(t)[(y(t)+p(t)y(τ(t)))′]γ)′+f(t,y(σ(t)))=0, where $\int ^{\infty }r^{-1/\gamma } ( s ) \,\mathrm{d}s= \infty $∫∞r−1/γ(s)ds=∞. Based on the comparison with first order delay equations and by employ the Riccati substitution technique, we improve and complement a number of well-known results. Some examples are provided to show the importance of these results.

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