scholarly journals A Philos-Type Oscillation Criteria for Fourth-Order Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 379 ◽  
Author(s):  
Omar Bazighifan ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Averaging Method ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
The Right ◽  
Type Oscillation ◽  
Oscillation Of Solutions

Some sufficient conditions are established for the oscillation of fourth order neutral differential equations of the form r t z ‴ t α ′ + q t x β σ t = 0 , where z t : = x t + p t x τ t . By using the technique of Riccati transformation and integral averaging method, we get conditions to ensure oscillation of solutions of this equation. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. Moreover, the importance of the obtained conditions is illustrated via some examples.

scholarly journals Oscillatory Behavior of Fourth-Order Differential Equations with Neutral Delay

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 371 ◽  
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Correct Direction ◽  
The Right

In this paper, new sufficient conditions for oscillation of fourth-order neutral differential equations are established. One objective of our paper is to further improve and complement some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.

scholarly journals Behavior of Non-Oscillatory Solutions of Fourth-Order Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 477 ◽  
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Omar Bazighifan
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fourth Order ◽  
Riccati Transformation ◽  
Oscillatory Solutions ◽  
Neutral Differential Equations ◽  
Future Developments ◽  
Generalized Riccati Transformation ◽  
Correct Direction ◽  
The Right

In this paper, we deal with the asymptotics and oscillation of the solutions of fourth-order neutral differential equations of the form r t z ‴ t α ′ + q t x α g t = 0 , where z t : = x t + p t x δ t . By using a generalized Riccati transformation, we study asymptotic behavior and derive some new oscillation criteria. Our results extend and improve some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.

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 Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 318
Author(s):  
Osama Moaaz ◽  
Amany Nabih ◽  
Hammad Alotaibi ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mixed Type ◽  
Relevant Literature ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

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.

On oscillatory fourth order nonlinear neutral differential equations – III

2018 ◽  
Vol 68 (6) ◽  
pp. 1385-1396 ◽  
Author(s):  
Arun Kumar Tripathy ◽  
Rashmi Rekha Mohanta
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Functional Differential ◽  
T Tau

Abstract In this paper, several sufficient conditions for oscillation of all solutions of fourth order functional differential equations of neutral type of the form $$\begin{array}{} \displaystyle \bigl(r(t)(y(t)+p(t)y(t-\tau))''\bigr)''+q(t)G\bigl(y(t-\sigma)\bigr)=0 \end{array}$$ are studied under the assumption $$\begin{array}{} \displaystyle \int\limits^{\infty}_{0}\frac{t}{r(t)}{\rm d} t =\infty \end{array}$$

scholarly journals Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1248 ◽  
Author(s):  
Omar Bazighifan ◽  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Delay Argument ◽  
The Right ◽  
Equations With Delay ◽  
Oscillatory Properties

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given.

Oscillation criteria for a class of nonlinear fourth order neutral differential equations

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
A. Tripathy
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Sufficient Conditions ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
T Tau ◽  
Positive Integers

AbstractIn this paper, sufficient conditions are obtained for oscillation of a class of nonlinear fourth order mixed neutral differential equations of the form (E)$$\left( {\frac{1} {{a\left( t \right)}}\left( {\left( {y\left( t \right) + p\left( t \right)y\left( {t - \tau } \right)} \right)^{\prime \prime } } \right)^\alpha } \right)^{\prime \prime } = q\left( t \right)f\left( {y\left( {t - \sigma _1 } \right)} \right) + r\left( t \right)g\left( {y\left( {t + \sigma _2 } \right)} \right)$$ under the assumption $$\int\limits_0^\infty {\left( {a\left( t \right)} \right)^{\tfrac{1} {\alpha }} dt} = \infty .$$ where α is a ratio of odd positive integers. (E) is studied for various ranges of p(t).

scholarly journals Improved Oscillation Criteria for 2nd-Order Neutral Differential Equations with Distributed Deviating Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 849
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Waad Muhsin ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
Oscillation Of Solutions

In this study, we establish new sufficient conditions for oscillation of solutions of second-order neutral differential equations with distributed deviating arguments. By employing a refinement of the Riccati transformations and comparison principles, we obtain new oscillation criteria that complement and improve some results reported in the literature. Examples are provided to illustrate the main results.

scholarly journals Oscillation Criteria of Solutions of Fourth-Order Neutral Differential Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 155
Author(s):  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Barakah Almarri ◽  
M. A. Aiyashi ◽  
Kamsing Nonlaopon
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Riccati Transformation ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we study the oscillation of solutions of fourth-order neutral delay differential equations in non-canonical form. By using Riccati transformation, we establish some new oscillation conditions. We provide some examples to examine the applicability of our results.

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