IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i18p2847-d1477545.html
   My bibliography  Save this article

Third-Order Noncanonical Neutral Delay Differential Equations: Nonexistence of Kneser Solutions via Myshkis Type Criteria

Author

Listed:
  • Gunasekaran Nithyakala

    (Department of Applied Mathematics and Computational Science, Thiagarajar College of Engineering, Madurai 625 015, Tamilnadu, India)

  • George E. Chatzarakis

    (Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, 15122 Marousi, Athens, Greece)

  • Govindasamy Ayyappan

    (Department of Mathematics, Government Arts and Science College, Pappireddipatti 636 905, Tamilnadu, India)

  • Ethiraju Thandapani

    (Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamilnadu, India)

Abstract

The purpose of this paper is to add some new asymptotic and oscillatory results for third-order neutral delay differential equations with noncanonical operators. Without assuming any extra conditions, by using the canonical transform technique, the studied equation is changed to a canonical type equation, and this reduces the number of classes of nonoscillatory solutions into two instead of four. Then, we obtain Myshkis type sufficient conditions for the nonexistence of Kneser type solutions for the studied equation. Finally, employing these newly obtained criteria, we provide conditions for the oscillation of all solutions of the studied equation. Examples are presented to illustrate the importance and the significance of the main results.

Suggested Citation

  • Gunasekaran Nithyakala & George E. Chatzarakis & Govindasamy Ayyappan & Ethiraju Thandapani, 2024. "Third-Order Noncanonical Neutral Delay Differential Equations: Nonexistence of Kneser Solutions via Myshkis Type Criteria," Mathematics, MDPI, vol. 12(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2847-:d:1477545
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/18/2847/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/18/2847/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tongxing Li & Chenghui Zhang & Guojing Xing, 2012. "Oscillation of Third-Order Neutral Delay Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, January.
    2. Taher S. Hassan & Bassant M. El-Matary, 2023. "Asymptotic Behavior and Oscillation of Third-Order Nonlinear Neutral Differential Equations with Mixed Nonlinearities," Mathematics, MDPI, vol. 11(2), pages 1-10, January.
    3. Džurina, Jozef & Jadlovská, Irena, 2018. "Oscillation of third-order differential equations with noncanonical operators," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 394-402.
    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. K. S. Vidhyaa & John R. Graef & E. Thandapani, 2020. "New Oscillation Results for Third-Order Half-Linear Neutral Differential Equations," Mathematics, MDPI, vol. 8(3), pages 1-9, March.
    2. Taher S. Hassan & Bassant M. El-Matary, 2023. "Asymptotic Behavior and Oscillation of Third-Order Nonlinear Neutral Differential Equations with Mixed Nonlinearities," Mathematics, MDPI, vol. 11(2), pages 1-10, January.
    3. Osama Moaaz & Yousef Alnafisah, 2023. "An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    4. Grace, Said R. & Jadlovská, Irena & Zafer, Agacik, 2019. "On oscillation of third-order noncanonical delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

    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:12:y:2024:i:18:p:2847-:d:1477545. 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.