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Symmetry
Volume 12
Issue 5
10.3390/sym12050764
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Article

New Comparison Theorems for the Even-Order Neutral Delay Differential Equation

by
Osama Moaaz
1,†,
Rami Ahmad El-Nabulsi
2,*,†,
Omar Bazighifan
3,4 and
Ali Muhib
1,5,†
1
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2
Athens Institute for Education and Research, Mathematics and Physics Divisions, 10671 Athens, Greece
3
Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
4
Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen
5
Department of Mathematics, Faculty of Education–Al-Nadirah, Ibb University, Ibb, Yemen
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2020, 12(5), 764; https://doi.org/10.3390/sym12050764
Submission received: 12 March 2020 / Revised: 8 April 2020 / Accepted: 9 April 2020 / Published: 6 May 2020
(This article belongs to the Special Issue Asymptotic Properties of Solutions of Difference and Differential Equations)
Versions Notes

Abstract

The aim of this study was to examine the asymptotic properties and oscillation of the even-order neutral differential equations. The results obtained are based on the Riccati transformation and the theory of comparison with first- and second-order delay equations. Our results improve and complement some well-known results. We obtain Hille and Nehari type oscillation criteria to ensure the oscillation of the solutions of the equation. One example is provided to illustrate these results.
Keywords: even-order differential equations; neutral delay; oscillation even-order differential equations; neutral delay; oscillation

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MDPI and ACS Style

Moaaz, O.; El-Nabulsi, R.A.; Bazighifan, O.; Muhib, A. New Comparison Theorems for the Even-Order Neutral Delay Differential Equation. Symmetry 2020, 12, 764. https://doi.org/10.3390/sym12050764

AMA Style

Moaaz O, El-Nabulsi RA, Bazighifan O, Muhib A. New Comparison Theorems for the Even-Order Neutral Delay Differential Equation. Symmetry. 2020; 12(5):764. https://doi.org/10.3390/sym12050764

Chicago/Turabian Style

Moaaz, Osama, Rami Ahmad El-Nabulsi, Omar Bazighifan, and Ali Muhib. 2020. "New Comparison Theorems for the Even-Order Neutral Delay Differential Equation" Symmetry 12, no. 5: 764. https://doi.org/10.3390/sym12050764

APA Style

Moaaz, O., El-Nabulsi, R. A., Bazighifan, O., & Muhib, A. (2020). New Comparison Theorems for the Even-Order Neutral Delay Differential Equation. Symmetry, 12(5), 764. https://doi.org/10.3390/sym12050764

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