IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i20p3217-d1498644.html
   My bibliography  Save this article

On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms

Author

Listed:
  • A. A. El-Gaber

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

  • M. M. A. El-Sheikh

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

  • Haytham M. Rezk

    (Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt)

  • Mohammed Zakarya

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia)

  • Ghada AlNemer

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

  • E. I. El-Saedy

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

Abstract

The oscillation and asymptotic behavior of solutions of a general class of damped second-order differential equations with several sub-linear neutral terms is considered. New sufficient conditions are established to fulfill a part of the gap in the oscillation theory for the case of sub-linear neutral equations. Our main results improve and generalize some of those recently published in the literature. Several examples are given to support our results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3217-:d:1498644
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/20/3217/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/20/3217/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, July.
    2. Agarwal, Ravi P. & Bohner, Martin & Li, Tongxing, 2015. "Oscillatory behavior of second-order half-linear damped dynamic equations," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 408-418.
    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.
    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. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    2. 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.
    3. Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    4. 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.
    5. 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.
    6. 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.
    7. Taher S. Hassan & Clemente Cesarano & Rami Ahmad El-Nabulsi & Waranont Anukool, 2022. "Improved Hille-Type Oscillation Criteria for Second-Order Quasilinear Dynamic Equations," Mathematics, MDPI, vol. 10(19), pages 1-18, October.
    8. 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.
    9. 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.
    10. H. A. Agwa & Ahmed M. M. Khodier & Heba M. Arafa, 2017. "Oscillation of Second-Order Nonlinear Mixed Neutral Dynamic Equations with Non Positive Neutral Term on Time Scales," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 3(2), pages 8-20, 02-2017.
    11. 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).
    12. 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.
    13. Taher S. Hassan & Qingkai Kong & Bassant M. El-Matary, 2023. "Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    14. Taher S. Hassan & Clemente Cesarano & Loredana Florentina Iambor & Amir Abdel Menaem & Naveed Iqbal & Akbar Ali, 2024. "New Oscillation Criteria for Sturm–Liouville Dynamic Equations with Deviating Arguments," Mathematics, MDPI, vol. 12(10), pages 1-11, May.
    15. 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.
    16. Rongrong Guo & Qingdao Huang & Qingmin Liu, 2021. "Some New Oscillation Criteria of Even-Order Quasi-Linear Delay Differential Equations with Neutral Term," Mathematics, MDPI, vol. 9(17), pages 1-11, August.
    17. 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.
    18. 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.
    19. Chatzarakis, G.E. & Džurina, J. & Jadlovská, I., 2019. "New oscillation criteria for second-order half-linear advanced differential equations," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 404-416.
    20. Karpuz, Başak, 2019. "Hille–Nehari theorems for dynamic equations with a time scale independent critical constant," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 336-351.

    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:20:p:3217-:d:1498644. 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.