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 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 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 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.

Oscillations of Second Order Neutral Differential Equations

1993 ◽  
Vol 36 (4) ◽  
pp. 485-496 ◽  
Author(s):  
Shigui Ruan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractIn this paper, we consider the oscillatory behavior of the second order neutral delay differential equationwhere t ≥ t0,T and σ are positive constants, a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.

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 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 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 New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

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