IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v346y2019icp336-351.html
   My bibliography  Save this article

Hille–Nehari theorems for dynamic equations with a time scale independent critical constant

Author

Listed:
  • Karpuz, Başak

Abstract

In this paper, we give Hille–Nehari test for nonoscillation/oscillation of the dynamic equation(rxΔ)Δ(t)+p(t)x(t)=0fort∈[t0,∞)T,where t0∈T,supT=∞,r∈Crd([t0,∞)T,R+) and p∈Crd([t0,∞)T,R0+). We show that the critical constant for this dynamic equation is 14 as in the well-known cases T=R and T=Z. We also present illustrating examples showing that the critical constant 14 is sharp on arbitrary time scales. With two different techniques, we extend our results to the dynamic equation(rxΔ)Δ(t)+p(t)xσ(t)=0fort∈[t0,∞)Tby preserving the constant 14. The second technique is new even for the discrete case T=Z.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:336-351
    DOI: 10.1016/j.amc.2018.09.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318308348
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.09.055?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Elena Braverman & Başak Karpuz, 2011. "Nonoscillation of Second-Order Dynamic Equations with Several Delays," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-34, April.
    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. Shao-Yan Zhang & Qi-Ru Wang, 2014. "Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-10, 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. 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.
    2. 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.
    3. 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).

    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 & 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.
    2. 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.
    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. Chandrasekaran, E. & Chatzarakis, George E. & Palani, G. & Thandapani, E., 2020. "Oscillation criteria for advanced difference equations of second order," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    5. Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    6. Yong Zhou & Bashir Ahmad & Ahmed Alsaedi, 2019. "Structure of Non-Oscillatory Solutions for Second Order Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 7(8), pages 1-12, July.
    7. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    8. Ya-Ru Zhu & Zhong-Xuan Mao & Jing-Feng Tian & Ya-Gang Zhang & Xin-Ni Lin, 2022. "Oscillation and Nonoscillatory Criteria of Higher Order Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 10(5), pages 1-17, February.
    9. 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).
    10. 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.
    11. 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.

    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:eee:apmaco:v:346:y:2019:i:c:p:336-351. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.