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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hail S. Alrashdi & Osama Moaaz & Khaled Alqawasmi & Mohammad Kanan & Mohammed Zakarya & Elmetwally M. Elabbasy, 2024. "Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case," Mathematics, MDPI, vol. 12(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1189-:d:1376440
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    References listed on IDEAS

    as
    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano, 2023. "On the Dynamical Behavior of Solitary Waves for Coupled Stochastic Korteweg–De Vries Equations," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    2. Taher S. Hassan & Qingkai Kong & Bassant M. El-Matary, 2023. "Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    Full references (including those not matched with items on IDEAS)

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