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Amended Criteria of Oscillation for Nonlinear Functional Dynamic Equations of Second-Order

Author

Listed:
  • 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)

  • Rami Ahmad El-Nabulsi

    (Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Athens Institute for Education and Research, Mathematics and Physics Divisions, 8 Valaoritou Street, Kolonaki, 10671 Athens, Greece)

  • Amir Abdel Menaem

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

Abstract

In this paper, the sharp Hille-type oscillation criteria are proposed for a class of second-order nonlinear functional dynamic equations on an arbitrary time scale, by using the technique of Riccati transformation and integral averaging method. The obtained results demonstrate an improvement in Hille-type compared with the results reported in the literature. Some examples are provided to illustrate the significance of the obtained results.

Suggested Citation

  • Taher S. Hassan & Rami Ahmad El-Nabulsi & Amir Abdel Menaem, 2021. "Amended Criteria of Oscillation for Nonlinear Functional Dynamic Equations of Second-Order," Mathematics, MDPI, vol. 9(11), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1191-:d:561497
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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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    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.

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