IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i6p995-d774927.html
   My bibliography  Save this article

Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions

Author

Listed:
  • Barakah Almarri

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

  • Ali Hasan Ali

    (Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
    Doctoral School of Mathematical and Computational Sciences, University of Debrecen, H-4002 Debrecen, Hungary)

  • António M. Lopes

    (LAETA/INEGI, Faculty of Engineering, University of Porto, 4099-002 Porto, Portugal)

  • Omar Bazighifan

    (Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen
    Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy)

Abstract

The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order linear differential equation without damping. The extended Riccati transformation, integral averaging approach, and comparison principles are used to provide some additional oscillatory criteria. An example demonstrates the efficacy of the acquired criteria.

Suggested Citation

  • Barakah Almarri & Ali Hasan Ali & António M. Lopes & Omar Bazighifan, 2022. "Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions," Mathematics, MDPI, vol. 10(6), pages 1-10, March.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:995-:d:774927
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/6/995/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/6/995/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chengmin Hou & Sui Sun Cheng, 2009. "Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-7, June.
    2. Saad Althobati & Omar Bazighifan & Mehmet Yavuz, 2021. "Some Important Criteria for Oscillation of Non-Linear Differential Equations with Middle Term," Mathematics, MDPI, vol. 9(4), pages 1-9, February.
    3. M. Bartušek & M. Cecchi & Z. Došlá & M. Marini, 2012. "Fourth-Order Differential Equation with Deviating Argument," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Uroosa Arshad & Mariam Sultana & Ali Hasan Ali & Omar Bazighifan & Areej A. Al-moneef & Kamsing Nonlaopon, 2022. "Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    3. Nikola Popović & Kemal Eren & Ana Savić & Soley Ersoy, 2023. "Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    4. Sorin Mureşan & Loredana Florentina Iambor & Omar Bazighifan, 2022. "New Applications of Perov’s Fixed Point Theorem," Mathematics, MDPI, vol. 10(23), pages 1-9, December.
    5. Ramasamy Vimala & Ramasamy Kodeeswaran & Robert Cep & Majella Jenvi Ignatia Krishnasamy & Meenakshi Awasthi & Govindasamy Santhakumar, 2023. "Oscillation of Nonlinear Neutral Delay Difference Equations of Fourth Order," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    6. Mnaouer Kachout & Clemente Cesarano & Amir Abdel Menaem & Taher S. Hassan & Belal A. Glalah, 2023. "Oscillation Criteria for Qusilinear Even-Order Differential Equations," Mathematics, MDPI, vol. 11(12), pages 1-11, June.
    7. 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.

    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. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. 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.

    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:10:y:2022:i:6:p:995-:d:774927. 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.