IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2021i1p86-d711941.html
   My bibliography  Save this article

Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

Author

Listed:
  • Yang-Cong Qiu

    (School of Humanities, Shunde Polytechnic, Foshan 528333, China
    These authors contributed equally to this work.)

  • Kuo-Shou Chiu

    (Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, José Pedro Alessandri 774, Santiago 7760197, Chile
    These authors contributed equally to this work.)

  • Said R. Grace

    (Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt
    These authors contributed equally to this work.)

  • Qingmin Liu

    (School of Control Science and Engineering, Shandong University, Jinan 250061, China
    These authors contributed equally to this work.)

  • Irena Jadlovská

    (Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Kosice, Slovakia
    These authors contributed equally to this work.)

Abstract

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

Suggested Citation

  • Yang-Cong Qiu & Kuo-Shou Chiu & Said R. Grace & Qingmin Liu & Irena Jadlovská, 2021. "Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 10(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:86-:d:711941
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/1/86/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/1/86/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. George E. Chatzarakis & Said R. Grace & Irena Jadlovská & Tongxing Li & Ercan Tunç, 2019. "Oscillation Criteria for Third-Order Emden–Fowler Differential Equations with Unbounded Neutral Coefficients," Complexity, Hindawi, vol. 2019, pages 1-7, August.
    2. Shyam Sundar Santra & Omar Bazighifan & Mihai Postolache, 2021. "New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms," Mathematics, MDPI, vol. 9(11), pages 1-9, May.
    3. 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.
    4. Kuo‐Shou Chiu & Tongxing Li, 2019. "Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments," Mathematische Nachrichten, Wiley Blackwell, vol. 292(10), pages 2153-2164, October.
    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. Shyam Sundar Santra & Abhay Kumar Sethi & Osama Moaaz & Khaled Mohamed Khedher & Shao-Wen Yao, 2021. "New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation," Mathematics, MDPI, vol. 9(10), pages 1-11, May.
    2. Shyam Sundar Santra & Omar Bazighifan & Mihai Postolache, 2021. "New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms," Mathematics, MDPI, vol. 9(11), pages 1-9, May.
    3. A. A. El-Gaber & M. M. A. El-Sheikh & Haytham M. Rezk & Mohammed Zakarya & Ghada AlNemer & E. I. El-Saedy, 2024. "On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms," Mathematics, MDPI, vol. 12(20), pages 1-16, October.
    4. Chiu, Kuo-Shou & Li, Tongxing, 2022. "New stability results for bidirectional associative memory neural networks model involving generalized piecewise constant delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 719-743.
    5. 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.
    6. Osama Moaaz & Rami Ahmad El-Nabulsi & Ali Muhib & Sayed K. Elagan & Mohammed Zakarya, 2021. "New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    7. Osama Moaaz & Ali Muhib & Shyam S. Santra, 2021. "An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    8. Fátima Cruz & Ricardo Almeida & Natália Martins, 2021. "Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    9. 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.
    10. Grace, Said R. & Negi, Shekhar Singh & Abbas, Syed, 2022. "New oscillatory results for non-linear delay dynamic equations with super-linear neutral term," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    11. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    12. Bazighifan, Omar, 2020. "On the oscillation of certain fourth-order differential equations with p-Laplacian like operator," Applied Mathematics and Computation, Elsevier, vol. 386(C).

    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:2021:i:1:p:86-:d:711941. 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.