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 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 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 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 New Oscillation Criteria for Neutral Delay Differential Equations of Fourth-Order

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1277
Author(s):  
Saeed Althubiti ◽  
Omar Bazighifan ◽  
Hammad Alotaibi ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Riccati Technique ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

New oscillatory properties for the oscillation of solutions to a class of fourth-order delay differential equations with several deviating arguments are established, which extend and generalize related results in previous studies. Some oscillation results are established by using the Riccati technique under the case of canonical coefficients. The symmetry plays an important and fundamental role in the study of the oscillation of solutions of the equations. Examples are given to prove the significance of the new theorems.

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 Simplified and improved criteria for oscillation of delay differential equations of fourth order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. Moaaz ◽  
A. Muhib ◽  
D. Baleanu ◽  
W. Alharbi ◽  
E. E. Mahmoud
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Interesting Point ◽  
All Solutions ◽  
Special Cases ◽  
Delay Differential ◽  
Noncanonical Operator

AbstractAn interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studying the noncanonical case. Therefore, this study aims to reduce the oscillation conditions of the fourth-order delay differential equations with a noncanonical operator. Moreover, the approach used gives more accurate results when applied to some special cases, as we explained in the examples.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

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