scholarly journals Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 656 ◽  
Author(s):  
Omar Bazighifan ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillatory Properties

This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equations, we will establish some new oscillation criteria for this equation. Some examples are considered to illustrate the main results.

scholarly journals New Oscillation Criteria for Advanced Differential Equations of Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 728 ◽  
Author(s):  
Omar Bazighifan ◽  
Hijaz Ahmad ◽  
Shao-Wen Yao
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Second Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Delayed Arguments

The main objective of this paper is to establish new oscillation results of solutions to a class of fourth-order advanced differential equations with delayed arguments. The key idea of our approach is to use the Riccati transformation and the theory of comparison with first and second-order delay equations. Four examples are provided 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 Improved Conditions for Oscillation of Functional Nonlinear Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 552 ◽  
Author(s):  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillation Criteria ◽  
Delay Differential ◽  
Oscillatory Properties

The aim of this work is to study oscillatory properties of a class of fourth-order delay differential equations. New oscillation criteria are obtained by using generalized Riccati transformations. 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 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 Oscillatory Properties of Solutions of Even-Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 212 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Rami Ahmad El-Nabulsi ◽  
Osama Moaaz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Even Order ◽  
Oscillatory Properties

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using Riccati transformation and the integral averaging technique, we obtain a new oscillation criteria. This new theorem complements and improves some known results from the literature. An example is provided to illustrate the main results.

scholarly journals Symmetry and Its Importance in the Oscillation of Solutions of Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 650
Author(s):  
Ahmed AlGhamdi ◽  
Clemente Cesarano ◽  
Barakah Almarri ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
First Order ◽  
Main Equation ◽  
Engineering Physics ◽  
Equations With Delay ◽  
Oscillation Of Solutions ◽  
Oscillatory Properties

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. The purpose of this article is to explore the oscillation of fourth-order differential equations with delay arguments. New Kamenev-type oscillatory properties are established, which are based on a suitable Riccati method to reduce the main equation into a first-order inequality. Our new results extend and simplify existing results in the previous studies. Examples are presented in order to clarify the main results.

scholarly journals Delay Differential Equations of Fourth-Order: Oscillation and Asymptotic Properties of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2015
Author(s):  
Omar Bazighifan ◽  
Maryam Al-Kandari ◽  
Khalil S. Al-Ghafri ◽  
F. Ghanim ◽  
Sameh Askar ◽  
...  
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Essential Role ◽  
Asymptotic Properties ◽  
Comparison Method ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
Delay Differential

In this work, by using the comparison method and Riccati transformation, we obtain some oscillation criteria of solutions of delay differential equations of fourth-order in canonical form. These criteria complement those results in the literature. We give two examples to illustrate the main results. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

scholarly journals A New Approach in the Study of Oscillation Criteria of Even-Order Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 197 ◽  
Author(s):  
Osama Moaaz ◽  
Jan Awrejcewicz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Delay Equations ◽  
Oscillation Criterion ◽  
New Approach ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Even Order ◽  
New Criterion

Based on the comparison with first-order delay equations, we establish a new oscillation criterion for a class of even-order neutral differential equations. Our new criterion improves a number of existing ones. An illustrative example is provided.

scholarly journals New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-Like Operators

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2584
Author(s):  
Omar Bazighifan ◽  
F. Ghanim ◽  
Jan Awrejcewicz ◽  
Khalil S. Al-Ghafri ◽  
Maryam Al-Kandari
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Comparison Method ◽  
Linear Differential Equations ◽  
Riccati Transformation ◽  
Linear Differential ◽  
Delay Differential ◽  
New Criteria ◽  
Oscillatory Properties

In this paper, new oscillatory properties for fourth-order delay differential equations with p-Laplacian-like operators are established, using the Riccati transformation and comparison method. Moreover, our results are an extension and complement to previous results in the literature. We provide some examples to examine the applicability of our results.

scholarly journals On the Oscillation Criteria for Fourth-Order p -Laplacian Differential Equations with Middle Term

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Dandan Yang ◽  
Chuanzhi Bai
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Second Order ◽  
Middle Term ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Oscillatory Properties

In this paper, we study the oscillatory properties of the solutions of a class of fourth-order p -Laplacian differential equations with middle term. The new oscillation criteria obtained by using the theory of comparison with first- and second-order differential equations and a refinement of the Riccati transformations. The results in this paper improve and generalize the corresponding results in the literatures. Three examples are provided to illustrate our results.

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