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 Oscillation and non-oscillation of some neutral differential equations of odd order

1992 ◽  
Vol 15 (3) ◽  
pp. 509-515 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Odd Order ◽  
Existence Criterion ◽  
Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

scholarly journals Oscillation theorems of solution of second-order neutral differential equations

2021 ◽  
Vol 6 (11) ◽  
pp. 12771-12779
Author(s):  
Ali Muhib ◽  
◽  
Hammad Alotaibi ◽  
Omar Bazighifan ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Second Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Theoretical Support ◽  
Functional Differential ◽  
Oscillation Theorems ◽  
New Criteria ◽  
Oscillation Of Solutions

<abstract><p>In this paper, we aim to explore the oscillation of solutions for a class of second-order neutral functional differential equations. We propose new criteria to ensure that all obtained solutions are oscillatory. The obtained results can be used to develop and provide theoretical support for and further develop the oscillation study for a class of second-order neutral differential equations. Finally, an illustrated example is given to demonstrate the effectiveness of our new criteria.</p></abstract>

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.

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.

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 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.

scholarly journals More Effective Criteria for Oscillation of Second-Order Differential Equations with Neutral Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 986
Author(s):  
Osama Moaaz ◽  
Mona Anis ◽  
Dumitru Baleanu ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
New Criteria ◽  
Oscillation Of Solutions

The motivation for this paper is to create new criteria for oscillation of solutions of second-order nonlinear neutral differential equations. In more than one respect, our results improve several related ones in the literature. As proof of the effectiveness of the new criteria, we offer more than one practical example.

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 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.

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.

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