Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case

Hail S. Alrashdi, Osama Moaaz (), Khaled Alqawasmi, Mohammad Kanan, Mohammed Zakarya and Elmetwally M. Elabbasy
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Hail S. Alrashdi: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Osama Moaaz: Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
Khaled Alqawasmi: Cyber Security Department, Zarqa University, Zarqa 13110, Jordan
Mohammad Kanan: Department of Industrial Engineering, College of Engineering, University of Business and Technology, Jeddah 21448, Saudi Arabia
Mohammed Zakarya: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Elmetwally M. Elabbasy: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2024, vol. 12, issue 8, 1-15

Abstract: This paper investigates the asymptotic and oscillatory properties of a distinctive class of third-order linear differential equations characterized by multiple delays in a noncanonical case. Employing the comparative method and the Riccati method, we introduce the novel and rigorous criteria to discern whether the solutions of the examined equation exhibit oscillatory behavior or tend toward zero. Our study contributes to the existing literature by presenting theories that extend and refine the understanding of these properties in the specified context. To validate our findings and demonstrate their applicability in a general setting, we offer two illustrative examples, affirming the robustness and validity of our proposed criteria.

Keywords: delay differential equations; asymptotic and oscillatory properties; third-order; noncanonical case (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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