scholarly journals Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yakun Wang ◽  
Fanwei Meng ◽  
Juan Gu
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Distributed Deviating Arguments ◽  
Generalized Riccati Transformation

AbstractOur objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example to illustrate the main results.

scholarly journals Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1021
Author(s):  
Marappan Sathish Kumar ◽  
Omar Bazighifan ◽  
Alanoud Almutairi ◽  
Dimplekumar N. Chalishajar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Riccati Transformation ◽  
Third Order ◽  
Transformation Techniques ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Integral Averaging Technique ◽  
Type Oscillation

The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the integral averaging technique. The established criteria improve, simplify and complement results that have been published recently in the literature. An example is also given to demonstrate the applicability of the obtained conditions.

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 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.

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