scholarly journals New results for oscillatory behavior of even-order half-linear delay differential equations

2013 ◽  
Vol 26 (2) ◽  
pp. 179-183 ◽  
Author(s):  
Chenghui Zhang ◽  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Linear Delay ◽  
Even Order ◽  
Delay Differential

Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms

2019 ◽  
Vol 69 (5) ◽  
pp. 1117-1126
Author(s):  
Said R. Grace ◽  
John R. Graef ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Linear Delay ◽  
Delay Differential

Abstract This article concerns the oscillatory behavior of solutions to second-order half-linear delay differential equations with mixed neutral terms. The authors present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated with examples.

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 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 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 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.

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