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 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 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 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 criteria of fourth-order quasi-linear differential equations with neutral term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Saeed Althubiti ◽  
Fahad Alsharari ◽  
Omar Bazighifan ◽  
George E. Chatzarakis
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Average Technique ◽  
Neutral Differential Equations ◽  
Linear Differential ◽  
Fourth Order Equations ◽  
Delay Differential ◽  
Integral Average

AbstractIn this article, we are interested in studying the asymptotic behavior of fourth-order neutral differential equations. Despite the growing interest in studying the oscillatory behavior of delay differential equations of second-order, fourth-order equations have received less attention. We get more than one criterion to check the oscillation by the generalized Riccati method and the integral average technique. Our results are an extension and complement to some results published in the literature. Examples are given to prove the significance of new theorems.

scholarly journals Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Chengmin Hou ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Third Order ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Linear Differential ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third-order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.

scholarly journals Criteria for the Nonexistence of Kneser Solutions of DDEs and Their Applications in Oscillation Theory

2021 ◽  
Vol 11 (1) ◽  
pp. 425
Author(s):  
Osama Moaaz ◽  
Ioannis Dassios ◽  
Haifa Bin Jebreen ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillation Theory ◽  
Oscillation Criteria ◽  
Delay Argument ◽  
Delay Differential ◽  
New Criteria

The objective of this study was to improve existing oscillation criteria for delay differential equations (DDEs) of the fourth order by establishing new criteria for the nonexistence of so-called Kneser solutions. The new criteria are characterized by taking into account the effect of delay argument. All previous relevant results have neglected the effect of the delay argument, so our results substantially improve the well-known results reported in the literature. The effectiveness of our new criteria is illustrated via an example.

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 More Effective Results for Testing Oscillation of Non-Canonical Neutral Delay Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1114
Author(s):  
Higinio Ramos ◽  
Osama Moaaz ◽  
Ali Muhib ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Interesting Problem ◽  
Neutral Delay ◽  
Canonical Operator ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
New Criteria

In this work, we address an interesting problem in studying the oscillatory behavior of solutions of fourth-order neutral delay differential equations with a non-canonical operator. We obtained new criteria that improve upon previous results in the literature, concerning more than one aspect. Some examples are presented to illustrate the importance of the new results.

scholarly journals Asymptotic and Oscillatory Properties of Noncanonical Delay Differential Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 259
Author(s):  
Osama Moaaz ◽  
Clemente Cesarano ◽  
Sameh Askar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Oscillatory Solutions ◽  
Even Order ◽  
Delay Differential ◽  
New Criteria ◽  
Oscillatory Properties

In this work, by establishing new asymptotic properties of non-oscillatory solutions of the even-order delay differential equation, we obtain new criteria for oscillation. The new criteria provide better results when determining the values of coefficients that correspond to oscillatory solutions. To explain the significance of our results, we apply them to delay differential equation of Euler-type.

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

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 628 ◽  
Author(s):  
Clemente Cesarano ◽  
Sandra Pinelas ◽  
Faisal Al-Showaikh ◽  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Asymptotic Properties ◽  
Riccati Transformation ◽  
Delay Differential ◽  
Oscillation Of Solutions ◽  
Comparison Technique

In the paper, we study the oscillation of fourth-order delay differential equations, the present authors used a Riccati transformation and the comparison technique for the fourth order delay differential equation, and that was compared with the oscillation of the certain second order differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. Some examples are also presented to test the strength and applicability of the results obtained.

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