scholarly journals On the Oscillation of Solutions of Differential Equations with Neutral Term

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2709
Author(s):  
Fatemah Mofarreh ◽  
Alanoud Almutairi ◽  
Omar Bazighifan ◽  
Mohammed A. Aiyashi ◽  
Alina-Daniela Vîlcu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Averaging Method ◽  
Oscillatory Behavior ◽  
Neutral Term ◽  
Even Order ◽  
Delay Differential ◽  
New Criteria ◽  
Oscillation Of Solutions ◽  
Comparison Technique

In this work, new criteria for the oscillatory behavior of even-order delay differential equations with neutral term are established by comparison technique, Riccati transformation and integral averaging method. The presented results essentially extend and simplify known conditions in the literature. To prove the validity of our results, we give some 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 Some New Oscillation Criteria of Even-Order Quasi-Linear Delay Differential Equations with Neutral Term

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2074
Author(s):  
Rongrong Guo ◽  
Qingdao Huang ◽  
Qingmin Liu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Type ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Linear Delay ◽  
Neutral Delay Differential Equations ◽  
Even Order ◽  
Delay Differential

The neutral delay differential equations have many applications in the natural sciences, technology, and population dynamics. In this paper, we establish several new oscillation criteria for a kind of even-order quasi-linear neutral delay differential equations. Comparing our results with those in the literature, our criteria solve more general delay differential equations with neutral type, and our results expand the range of neutral term coefficient. Some examples are given to illustrate our conclusions.

scholarly journals Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term

2019 ◽  
Vol 39 (1) ◽  
pp. 39-47 ◽  
Author(s):  
John R. Graef ◽  
Said R. Grace ◽  
Ercan Tunç
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Order Linear ◽  
First Order ◽  
Neutral Term ◽  
Linear Delay ◽  
Even Order ◽  
A New Technique ◽  
Delay Differential

The authors present a new technique for the linearization of even-order nonlinear differential equations with a sublinear neutral term. They establish some new oscillation criteria via comparison with higher-order linear delay differential inequalities as well as with first-order linear delay differential equations whose oscillatory characters are known. Examples are provided to illustrate the theorems.

scholarly journals Odd-order differential equations with deviating arguments: asymptomatic behavior and oscillation

2021 ◽  
Vol 19 (2) ◽  
pp. 1411-1425
Author(s):  
A. Muhib ◽  
◽  
I. Dassios ◽  
D. Baleanu ◽  
S. S. Santra ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Deviating Arguments ◽  
Odd Order ◽  
Even Order ◽  
Delay Differential

<abstract><p>Despite the growing interest in studying the oscillatory behavior of delay differential equations of even-order, odd-order equations have received less attention. In this work, we are interested in studying the oscillatory behavior of two classes of odd-order equations with deviating arguments. We get more than one criterion to check the oscillation in different methods. Our results are an extension and complement to some results published in the literature.</p></abstract>

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 oscillation theorems for a class of even-order neutral delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mona Anis ◽  
Osama Moaaz
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Delay Differential Equations ◽  
Even Order ◽  
Delay Differential ◽  
Oscillation Theorems ◽  
Appl Math

AbstractIn this work, we study the oscillatory behavior of even-order neutral delay differential equations $\upsilon ^{n}(l)+b(l)u(\eta (l))=0$ υ n ( l ) + b ( l ) u ( η ( l ) ) = 0 , where $l\geq l_{0}$ l ≥ l 0 , $n\geq 4$ n ≥ 4 is an even integer and $\upsilon =u+a ( u\circ \mu ) $ υ = u + a ( u ∘ μ ) . By deducing a new iterative relationship between the solution and the corresponding function, new oscillation criteria are established that improve those reported in (T. Li, Yu.V. Rogovchenko in Appl. Math. Lett. 61:35–41, 2016).

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 New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1971
Author(s):  
Osama Moaaz ◽  
Clemente Cesarano
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Positive Solutions ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Even Order ◽  
Delay Differential ◽  
New Criteria ◽  
Noncanonical Operator

In this study, new asymptotic properties of positive solutions of the even-order delay differential equation with the noncanonical operator are established. The new properties are of an iterative nature, which allows it to be applied several times. Moreover, we use these properties to obtain new criteria for the oscillation of the solutions of the studied equation using the principles of comparison.

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