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 Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order

2021 ◽  
Vol 5 (3) ◽  
pp. 95
Author(s):  
M. Sathish Kumar ◽  
R. Elayaraja ◽  
V. Ganesan ◽  
Omar Bazighifan ◽  
Khalifa Al-Shaqsi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Qualitative Behavior ◽  
Riccati Transformation ◽  
Third Order ◽  
Average Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Unbounded Solutions ◽  
Generalized Riccati Transformation ◽  
Integral Average

New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.

scholarly journals Boundedness and oscillation of third order neutral differential equations

2009 ◽  
Vol 43 (1) ◽  
pp. 137-144 ◽  
Author(s):  
Božena Mihalíková ◽  
Eva Kostiková
Keyword(s):  
Differential Equations ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
The Relationship ◽  
Oscillation Of Solutions

Abstract The relationship between boundedness and oscillation of solutions of the third order neutral differential equations are presented.

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 Improved Oscillation Criteria for 2nd-Order Neutral Differential Equations with Distributed Deviating Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 849
Author(s):  
Osama Moaaz ◽  
Rami Ahmad El-Nabulsi ◽  
Waad Muhsin ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Comparison Principles ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
Oscillation Of Solutions

In this study, we establish new sufficient conditions for oscillation of solutions of second-order neutral differential equations with distributed deviating arguments. By employing a refinement of the Riccati transformations and comparison principles, we obtain new oscillation criteria that complement and improve some results reported in the literature. Examples are provided to illustrate the main results.

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