IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p235-d486733.html
   My bibliography  Save this article

Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations

Author

Listed:
  • Zuzana Pátíková

    (Department of Mathematics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 760 05 Zlín, Czech Republic)

  • Simona Fišnarová

    (Department of Mathematics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic)

Abstract

We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is ensured by the divergence of a certain integral. The second one provides the condition of the oscillation in the case where the relevant integral converges, and it can be seen as a Hille–Nehari-type criterion. The use of the results is shown in several examples, in which the Euler-type equation and its perturbations are considered.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:235-:d:486733
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/235/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/235/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    2. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    3. 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.
    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.
    5. Munirah Aldiaiji & Belgees Qaraad & Loredana Florentina Iambor & Safi S. Rabie & Elmetwally M. Elabbasy, 2023. "Oscillation of Third-Order Differential Equations with Advanced Arguments," Mathematics, MDPI, vol. 12(1), pages 1-12, December.
    6. 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.
    7. 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.
    8. 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.
    9. Osama Moaaz & Mona Anis & Dumitru Baleanu & Ali Muhib, 2020. "More Effective Criteria for Oscillation of Second-Order Differential Equations with Neutral Arguments," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    10. 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.

    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:9:y:2021:i:3:p:235-:d:486733. 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.