IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i4p635-d1591652.html
   My bibliography  Save this article

Iterative Kneser-Type Criteria for Oscillation of Half-Linear Second-Order Advanced Dynamic Equations

Author

Listed:
  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Bassant M. El-Matary

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

  • Ioan-Lucian Popa

    (Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
    Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania)

  • Mouataz Billah Mesmouli

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia)

  • Ismoil Odinaev

    (Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia)

  • Yousef Jawarneh

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia)

Abstract

This work aims to develop new iterative Kneser-type criteria for determining the oscillatory behaviour of half-linear second-order advanced dynamic equations on arbitrary unbounded-above time scales T . The results extend and refine previously established criteria for these equations while also generalising classical criteria for corresponding ordinary dynamic equations. This study provides a broader and more flexible approach to analysing such systems by introducing iterative methods. Several examples are included to demonstrate the accuracy, usefulness, and adaptability.

Suggested Citation

  • Taher S. Hassan & Bassant M. El-Matary & Ioan-Lucian Popa & Mouataz Billah Mesmouli & Ismoil Odinaev & Yousef Jawarneh, 2025. "Iterative Kneser-Type Criteria for Oscillation of Half-Linear Second-Order Advanced Dynamic Equations," Mathematics, MDPI, vol. 13(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:635-:d:1591652
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/4/635/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/4/635/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Taher S. Hassan & Yuangong Sun & Amir Abdel Menaem, 2020. "Improved Oscillation Results for Functional Nonlinear Dynamic Equations of Second Order," Mathematics, MDPI, vol. 8(11), pages 1-19, October.
    3. 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.
    4. 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.
    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. 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.
    2. Taher S. Hassan & Rami Ahmad El-Nabulsi & Naveed Iqbal & Amir Abdel Menaem, 2024. "New Criteria for Oscillation of Advanced Noncanonical Nonlinear Dynamic Equations," Mathematics, MDPI, vol. 12(6), pages 1-13, March.
    3. Taher S. Hassan & Mnaouer Kachout & Bassant M. El-Matary & Loredana Florentina Iambor & Ismoil Odinaev & Akbar Ali, 2024. "Improved Hille-Type and Ohriska-Type Criteria for Half-Linear Third-Order Dynamic Equations," Mathematics, MDPI, vol. 12(23), pages 1-18, November.
    4. 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.
    5. 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.
    6. 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.
    7. Zuzana Pátíková & Simona Fišnarová, 2021. "Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    8. Yingying Wang & Zhinan Xia, 2023. "Lipschitz Stability in Terms of Two Measures for Kurzweil Equations and Applications," Mathematics, MDPI, vol. 11(9), pages 1-20, April.
    9. Taher S. Hassan & Rabie A. Ramadan & Zainab Alsheekhhussain & Ahmed Y. Khedr & Amir Abdel Menaem & Ismoil Odinaev, 2022. "Improved Hille Oscillation Criteria for Nonlinear Functional Dynamic Equations of Third-Order," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    10. Hail S. Alrashdi & Osama Moaaz & Khaled Alqawasmi & Mohammad Kanan & Mohammed Zakarya & Elmetwally M. Elabbasy, 2024. "Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case," Mathematics, MDPI, vol. 12(8), pages 1-15, April.
    11. Taher S. Hassan & Qingkai Kong & Rami Ahmad El-Nabulsi & Waranont Anukool, 2022. "New Hille Type and Ohriska Type Criteria for Nonlinear Third-Order Dynamic Equations," Mathematics, MDPI, vol. 10(21), pages 1-12, November.
    12. Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    13. Omar Bazighifan & Nawa Alshammari & Khalil S. Al-Ghafri & Loredana Florentina Iambor, 2024. "Differential Equations of Fourth-Order with p -Laplacian-like Operator: Oscillation Theorems," Mathematics, MDPI, vol. 12(22), pages 1-10, November.
    14. Hail S. Alrashdi & Wedad Albalawi & Ali Muhib & Osama Moaaz & Elmetwally M. Elabbasy, 2024. "Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations," Mathematics, MDPI, vol. 12(11), pages 1-16, June.
    15. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    16. 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.
    17. Osama Moaaz & Belgees Qaraad & Rami Ahmad El-Nabulsi & Omar Bazighifan, 2020. "New Results for Kneser Solutions of Third-Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 8(5), pages 1-12, May.
    18. Omar Bazighifan & Clemente Cesarano, 2019. "Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    19. 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.
    20. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(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:13:y:2025:i:4:p:635-:d:1591652. 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.