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 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 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 Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yakun Wang ◽  
Fanwei Meng ◽  
Juan Gu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation

AbstractOur objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example to illustrate the main results.

scholarly journals Emden–Fowler-type neutral differential equations: oscillatory properties of solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Omar Bazighifan ◽  
Alanoud Almutairi
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Comparison Method ◽  
Riccati Transformation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Delay Differential ◽  
Oscillatory Properties

AbstractIn this paper, we study the oscillation of a class of fourth-order Emden–Fowler delay differential equations with neutral term. Using the Riccati transformation and comparison method, we establish several new oscillation conditions. These new conditions complement a number of results in the literature. We give examples to illustrate our main results.

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.

scholarly journals Oscillation results for a certain class of fourth-order nonlinear delay differential equations

2021 ◽  
Vol 40 (2) ◽  
pp. 505-523
Author(s):  
Osama Moaaz ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Transformation Technique ◽  
Neutral Differential Equations ◽  
Delay Argument ◽  
Generalized Riccati Transformation ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Equations With Delay ◽  
Nonlinear Delay

In this work, we study the oscillation of the fourth order neutral differential equations with delay argument. By means of generalized Riccati transformation technique, we obtain new oscillation criteria for oscillation of this equation. An example is given to clarify the main results in this paper.

scholarly journals Asymptotic and Oscillatory Behavior of Solutions of a Class of Higher Order Differential Equation

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1434 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Clemente Cesarano ◽  
Omar Bazighifan ◽  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Future Developments ◽  
Correct Direction ◽  
Delay Differential ◽  
The Right

The objective of this paper is to study asymptotic behavior of a class of higher-order delay differential equations with a p-Laplacian like operator. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and show us the correct direction for future developments. New oscillation criteria are obtained by employing a refinement of the generalized Riccati transformations and comparison principles. This new theorem complements and improves a number of results reported in the literature. Some examples are provided to illustrate the main results.

scholarly journals Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order

2021 ◽  
Vol 5 (3) ◽  
pp. 95
Author(s):  
M. Sathish Kumar ◽  
R. Elayaraja ◽  
V. Ganesan ◽  
Omar Bazighifan ◽  
Khalifa Al-Shaqsi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Qualitative Behavior ◽  
Riccati Transformation ◽  
Third Order ◽  
Average Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Unbounded Solutions ◽  
Generalized Riccati Transformation ◽  
Integral Average

New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

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.

scholarly journals Oscillation for a Class of Right Fractional Differential Equations on the Right Half Line with Damping

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Hui Liu ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Half Line ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation ◽  
Fractional Differential ◽  
The Right

In this paper, we discuss a class of fractional differential equations of the form D-α+1y(t)·D-αy(t)-p(t)f(D-αy(t))+q(t)h∫t∞(s-t)-αy(s)ds=0.D-αy(t) is the Liouville right-sided fractional derivative of order α∈(0,1). We obtain some oscillation criteria for the equation by employing a generalized Riccati transformation technique. Some examples are given to illustrate the significance of our results.

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