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Volume 13
Issue 10
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms

by
Asma Al-Jaser
1,
Insaf F. Ben Saoud
2,
Higinio Ramos
3,4,* and
Belgees Qaraad
5,*
1
Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2
Department of Mathematics, Faculty of Education, University of Benghazi, Benghazi 1308, Libya
3
Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
4
Department of Mathematics, Escuela Politecnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain
5
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
*
Authors to whom correspondence should be addressed.
Axioms 2024, 13(10), 703; https://doi.org/10.3390/axioms13100703 (registering DOI)
Submission received: 2 September 2024 / Revised: 9 October 2024 / Accepted: 10 October 2024 / Published: 11 October 2024
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
Versions Notes

Abstract

In this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for excluding increasing positive solutions and decreasing positive solutions so that the resulting criteria are easier to apply than other criteria that have appeared in the literature. We have obtained new oscillation criteria that hold up more robustly upon application. Some examples are presented to illustrate the significance of our main findings.
Keywords: third-order differential equation; oscillation; nonoscillation; delay third-order differential equation; oscillation; nonoscillation; delay

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MDPI and ACS Style

Al-Jaser, A.; Saoud, I.F.B.; Ramos, H.; Qaraad, B. Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms. Axioms 2024, 13, 703. https://doi.org/10.3390/axioms13100703

AMA Style

Al-Jaser A, Saoud IFB, Ramos H, Qaraad B. Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms. Axioms. 2024; 13(10):703. https://doi.org/10.3390/axioms13100703

Chicago/Turabian Style

Al-Jaser, Asma, Insaf F. Ben Saoud, Higinio Ramos, and Belgees Qaraad. 2024. "Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms" Axioms 13, no. 10: 703. https://doi.org/10.3390/axioms13100703

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