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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
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    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)

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