scholarly journals Oscillation criteria for even order nonlinear neutral differential equations

2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yibing Sun ◽  
Zhenlai Han ◽  
Shurong Sun ◽  
Chao Zhang
Keyword(s):  
Differential Equations ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Even Order

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.

Improved oscillation criteria for even-order neutral differential equations

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
George E. Chatzarakis ◽  
Irena Jadlovská ◽  
Ercan Tunç
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Future Research ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Even Order ◽  
Appl Math

Abstract New sufficient conditions for the oscillation of all solutions to a class of even-order differential equations with bounded and unbounded neutral coefficients are established, which refine, significantly simplify and generalize those in [T. Li and Y. V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett. 61 2016, 35–41]. Examples are provided to illustrate the results and suggestions for future research are included.

scholarly journals A New Approach in the Study of Oscillation Criteria of Even-Order Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 197 ◽  
Author(s):  
Osama Moaaz ◽  
Jan Awrejcewicz ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Delay Equations ◽  
Oscillation Criterion ◽  
New Approach ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
First Order ◽  
Even Order ◽  
New Criterion

Based on the comparison with first-order delay equations, we establish a new oscillation criterion for a class of even-order neutral differential equations. Our new criterion improves a number of existing ones. An illustrative example is provided.

scholarly journals Oscillation Criteria of Higher-order Neutral Differential Equations with Several Deviating Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 412 ◽  
Author(s):  
Osama Moaaz ◽  
Ioannis Dassios ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Riccati Transformation ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Type Criterion ◽  
Even Order

This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using the technique of Riccati transformation and comparison principles with the second-order differential equations, we obtain a new Philos-type criterion. Our results extend and improve some known results in the literature. An example is given to illustrate our main results.

scholarly journals An Approach for Studying Asymptotic Properties of Solutions of Neutral Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 555 ◽  
Author(s):  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Even Order ◽  
Correct Direction ◽  
Type Oscillation

The paper is devoted to the study of oscillation of even-order neutral differential equations. New Kamenev-type oscillation criteria are established, and they essentially improve and complement some the well-known results reported in the literature. Ideas of symmetry help us determine the correct ways to study these topics and show us the correct direction, because they are often invisible. To illustrate the main results, some examples are mentioned.

Sign in / Sign up

Export Citation Format

Share Document