scholarly journals New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2177
Author(s):  
Saeed Althubiti ◽  
Ibtisam Aldawish ◽  
Jan Awrejcewicz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Essential Role ◽  
Differential Inequalities ◽  
Riccati Transformation ◽  
Neutral Differential Equations ◽  
First Order ◽  
Neutral Term ◽  
Even Order ◽  
Oscillation Of Solutions

The objective of this study is to establish new sufficient criteria for oscillation of solutions of even-order delay Emden-Fowler differential equations with neutral term rıyı+mıygın−1γ′+∑i=1jqiıyγμiı=0. We use Riccati transformation and the comparison with first-order differential inequalities to obtain theses criteria. Moreover, the presented oscillation conditions essentially simplify and extend known criteria in the literature. To show the importance of our results, we provide some examples. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

scholarly journals Third-order neutral differential equations of the mixed type: Oscillatory and asymptotic behavior

2021 ◽  
Vol 19 (2) ◽  
pp. 1649-1658
Author(s):  
B. Qaraad ◽  
◽  
O. Moaaz ◽  
D. Baleanu ◽  
S. S. Santra ◽  
...  
Keyword(s):  
Differential Equations ◽  
Mixed Type ◽  
Differential Inequalities ◽  
Riccati Transformation ◽  
Third Order ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
New Criteria ◽  
Comparison Technique

<abstract><p>In this work, by using both the comparison technique with first-order differential inequalities and the Riccati transformation, we extend this development to a class of third-order neutral differential equations of the mixed type. We present new criteria for oscillation of all solutions, which improve and extend some existing ones in the literature. In addition, we provide an example to illustrate our results.</p></abstract>

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 Oscillation and non-oscillation of some neutral differential equations of odd order

1992 ◽  
Vol 15 (3) ◽  
pp. 509-515 ◽  
Author(s):  
B. S. Lalli ◽  
B. G. Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solution ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
Neutral Term ◽  
Odd Order ◽  
Existence Criterion ◽  
Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

scholarly journals Oscillation of even-order neutral differential equations via comparison principles

2014 ◽  
Vol 30 (3) ◽  
pp. 293-300
Author(s):  
J. DZURINA ◽  
◽  
B. BACULIKOVA ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Higher Order ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
First Order ◽  
Even Order ◽  
Delay Differential

In the paper we offer oscillation criteria for even-order neutral differential equations, where z(t) = x(t) + p(t)x(τ(t)). Establishing a generalization of Philos and Staikos lemma, we introduce new comparison principles for reducing the examination of the properties of the higher order differential equation onto oscillation of the first order delay differential equations. The results obtained are easily verifiable.

scholarly journals New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 454 ◽  
Author(s):  
Osama Moaaz ◽  
Shigeru Furuichi ◽  
Ali Muhib
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Comparison Theorems ◽  
Differential Inequalities ◽  
Neutral Differential Equations ◽  
First Order ◽  
A New Technique ◽  
Equations With Delay ◽  
Higher Order Differential Equations ◽  
First Order Differential Equations

In this work, we present a new technique for the oscillatory properties of solutions of higher-order differential equations. We set new sufficient criteria for oscillation via comparison with higher-order differential inequalities. Moreover, we use the comparison with first-order differential equations. Finally, we provide an example to illustrate the importance of the results.

scholarly journals Oscillatory Properties of Solutions of Even-Order Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 212 ◽  
Author(s):  
Elmetwally M. Elabbasy ◽  
Rami Ahmad El-Nabulsi ◽  
Osama Moaaz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Even Order ◽  
Oscillatory Properties

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using Riccati transformation and the integral averaging technique, we obtain a new oscillation criteria. This new theorem complements and improves some known results from the literature. An example is provided to illustrate the main results.

scholarly journals Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1485
Author(s):  
M. Sathish Kumar ◽  
Omar Bazighifan ◽  
Khalifa Al-Shaqsi ◽  
Fongchan Wannalookkhee ◽  
Kamsing Nonlaopon
Keyword(s):  
Differential Equations ◽  
Essential Role ◽  
Third Order ◽  
Average Technique ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Unbounded Solutions ◽  
Riccati Substitution ◽  
Integral Average ◽  
Oscillation Of Solutions

Symmetry plays an essential role in determining the correct methods for the oscillatory properties of solutions to differential equations. This paper examines some new oscillation criteria for unbounded solutions of third-order neutral differential equations of the form (r2(ς)((r1(ς)(z′(ς))β1)′)β2)′ + ∑i=1nqi(ς)xβ3(ϕi(ς))=0. New oscillation results are established by using generalized Riccati substitution, an integral average technique in the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

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.

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