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Improved Oscillation Results for Functional Nonlinear Dynamic Equations of Second Order

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  • Taher S. Hassan

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    These authors contributed equally to this work.)

  • Yuangong Sun

    (School of Mathematical Sciences, University of Jinan, Jinan 250022, China
    These authors contributed equally to this work.)

  • Amir Abdel Menaem

    (Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
    These authors contributed equally to this work.)

Abstract

In this paper, the functional dynamic equation of second order is studied on an arbitrary time scale under milder restrictions without the assumed conditions in the recent literature. The Nehari, Hille, and Ohriska type oscillation criteria of the equation are investigated. The presented results confirm that the study of the equation in this formula is superior to other previous studies. Some examples are addressed to demonstrate the finding.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1897-:d:438065
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    References listed on IDEAS

    as
    1. Yuangong Sun & Taher S. Hassan, 2014. "Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, April.
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    Citations

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    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 & 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. Taher S. Hassan & Martin Bohner & Iambor Loredana Florentina & Amir Abdel Menaem & Mouataz Billah Mesmouli, 2023. "New Criteria of Oscillation for Linear Sturm–Liouville Delay Noncanonical Dynamic Equations," Mathematics, MDPI, vol. 11(23), pages 1-9, December.
    4. Osama Moaaz & Clemente Cesarano & Barakah Almarri, 2023. "An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications," Mathematics, MDPI, vol. 11(7), pages 1-14, April.
    5. 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.
    6. 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.
    7. 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.

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