IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i3p494-d1581586.html
   My bibliography  Save this article

On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation

Author

Listed:
  • Mohamed Mazen

    (Department of Mathematics, University College for Women, Ain Shams University, Cairo 11566, Egypt)

  • Mohamed M. A. El-Sheikh

    (Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511, Egypt)

  • Samah Euat Tallah

    (Basic Science Department, Higher Institute of Management Science & Foreign Trade, Cairo 11765, Egypt)

  • Gamal A. F. Ismail

    (Department of Mathematics, University College for Women, Ain Shams University, Cairo 11566, Egypt)

Abstract

This paper deals with the oscillatory behavior of solutions of a general class of fourth-order non-linear delay differential equations. New oscillation criteria are established using Riccati transformation and a Philos-type technique. The obtained results not only improve and extend some published results in the literature, but also relax some traditional conditions on the function ψ ( χ ( ι ) ) . Three examples are provided to illustrate the main results.

Suggested Citation

  • Mohamed Mazen & Mohamed M. A. El-Sheikh & Samah Euat Tallah & Gamal A. F. Ismail, 2025. "On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation," Mathematics, MDPI, vol. 13(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:494-:d:1581586
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/3/494/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/3/494/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Osama Moaaz & Ioannis Dassios & Omar Bazighifan, 2020. "Oscillation Criteria of Higher-order Neutral Differential Equations with Several Deviating Arguments," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Salah Benhiouna & Azzeddine Bellour & Reemah Alhuzally & Ahmad M. Alghamdi, 2024. "Existence of Solutions for Generalized Nonlinear Fourth-Order Differential Equations," Mathematics, MDPI, vol. 12(24), pages 1-10, December.
    3. Nikolay D. Dimitrov & Jagan Mohan Jonnalagadda, 2024. "Existence and Nonexistence Results for a Fourth-Order Boundary Value Problem with Sign-Changing Green’s Function," Mathematics, MDPI, vol. 12(16), pages 1-12, August.
    4. Agarwal, Ravi P. & Zhang, Chenghui & Li, Tongxing, 2016. "Some remarks on oscillation of second order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 178-181.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Salah Benhiouna & Azzeddine Bellour & Reemah Alhuzally & Ahmad M. Alghamdi, 2024. "Existence of Solutions for Generalized Nonlinear Fourth-Order Differential Equations," Mathematics, MDPI, vol. 12(24), pages 1-10, December.
    2. Taher S. Hassan & Rabie A. Ramadan & Zainab Alsheekhhussain & Ahmed Y. Khedr & Amir Abdel Menaem & Ismoil Odinaev, 2022. "Improved Hille Oscillation Criteria for Nonlinear Functional Dynamic Equations of Third-Order," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    3. Asma Al-Jaser & Belgees Qaraad & Omar Bazighifan & Loredana Florentina Iambor, 2023. "Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    4. Maryam Al-Kandari, 2023. "Conditions for the Oscillation of Solutions to Neutral Differential Equations of Higher Order," Mathematics, MDPI, vol. 11(24), pages 1-9, December.
    5. Taher S. Hassan & Qingkai Kong & Rami Ahmad El-Nabulsi & Waranont Anukool, 2022. "New Hille Type and Ohriska Type Criteria for Nonlinear Third-Order Dynamic Equations," Mathematics, MDPI, vol. 10(21), pages 1-12, November.
    6. Haifeng Tian & Rongrong Guo, 2024. "Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations," Mathematics, MDPI, vol. 12(10), pages 1-15, May.
    7. Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    8. Osama Moaaz & Ioannis Dassios & Omar Bazighifan & Ali Muhib, 2020. "Oscillation Theorems for Nonlinear Differential Equations of Fourth-Order," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    9. Awatif A. Hindi & Osama Moaaz & Clemente Cesarano & Wedad R. Alharbi & Mohamed A. Abdou, 2021. "Noncanonical Neutral DDEs of Second-Order: New Sufficient Conditions for Oscillation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    10. Shyam Sundar Santra & Rami Ahmad El-Nabulsi & Khaled Mohamed Khedher, 2021. "Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator," Mathematics, MDPI, vol. 9(12), pages 1-9, June.
    11. Osama Moaaz & Clemente Cesarano, 2021. "New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application," Mathematics, MDPI, vol. 9(16), pages 1-9, August.
    12. Jozef Dzurina, 2024. "Oscillation of Bounded Solutions of Delay Differential Equations," Mathematics, MDPI, vol. 13(1), pages 1-8, December.
    13. Omar Bazighifan & Mihai Postolache, 2020. "Improved Conditions for Oscillation of Functional Nonlinear Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    14. Alanoud Almutairi & Ali Hasan Ali & Omar Bazighifan & Loredana Florentina Iambor, 2023. "Oscillatory Properties of Fourth-Order Advanced Differential Equations," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    15. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    16. Zuhur Alqahtani & Belgees Qaraad & Areej Almuneef & Higinio Ramos, 2024. "Asymptotic and Oscillatory Analysis of Second-Order Differential Equations with Distributed Deviating Arguments," Mathematics, MDPI, vol. 12(22), pages 1-19, November.
    17. Omar Bazighifan & Ioannis Dassios, 2020. "Riccati Technique and Asymptotic Behavior of Fourth-Order Advanced Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    18. Jozef Džurina & Said R. Grace & Irena Jadlovská & Tongxing Li, 2020. "Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 910-922, May.
    19. Omar Bazighifan & Clemente Cesarano, 2019. "Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    20. Marappan Sathish Kumar & Omar Bazighifan & Alanoud Almutairi & Dimplekumar N. Chalishajar, 2021. "Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms," Mathematics, MDPI, vol. 9(9), pages 1-9, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:494-:d:1581586. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.