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Asymptotic and Oscillatory Analysis of Fourth-Order Nonlinear Differential Equations with p -Laplacian-like Operators and Neutral Delay Arguments

Author

Listed:
  • Mansour Alatwi

    (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)

  • Wedad Albalawi

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Fahd Masood

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Hamdy El-Metwally

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples.

Suggested Citation

  • Mansour Alatwi & Osama Moaaz & Wedad Albalawi & Fahd Masood & Hamdy El-Metwally, 2024. "Asymptotic and Oscillatory Analysis of Fourth-Order Nonlinear Differential Equations with p -Laplacian-like Operators and Neutral Delay Arguments," Mathematics, MDPI, vol. 12(3), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:470-:d:1331529
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    References listed on IDEAS

    as
    1. Osama Moaaz & Clemente Cesarano & Barakah Almarri, 2023. "An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications," Mathematics, MDPI, vol. 11(7), pages 1-14, April.
    2. Osama Moaaz & Jan Awrejcewicz & Ali Muhib, 2020. "Establishing New Criteria for Oscillation of Odd-Order Nonlinear Differential Equations," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    3. Bohner, Martin & Grace, Said R. & Sağer, Ilgin & Tunç, Ercan, 2016. "Oscillation of third-order nonlinear damped delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 21-32.
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    Cited by:

    1. Omar Bazighifan & Nawa Alshammari & Khalil S. Al-Ghafri & Loredana Florentina Iambor, 2024. "Differential Equations of Fourth-Order with p -Laplacian-like Operator: Oscillation Theorems," Mathematics, MDPI, vol. 12(22), pages 1-10, November.

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