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New Oscillation Criteria for Sturm–Liouville Dynamic Equations with Deviating Arguments

Author

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  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

  • Loredana Florentina Iambor

    (Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr.1, 410087 Oradea, Romania)

  • Amir Abdel Menaem

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

  • Naveed Iqbal

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Akbar Ali

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

Abstract

The aim of this study is to refine the known Riccati transformation technique to provide new oscillation criteria for solutions to second-order dynamic equations over time. It is important to note that the convergence or divergence of some improper integrals on time scales depends not only on the integration function but also on the integration time scale. Therefore, there has been a motivation to find new oscillation criteria that can be applicable regardless of whether ∫ ζ 0 ∞ Δ ξ a ( ξ ) is convergent or divergent, in contrast to what has been followed in most previous works in the literature. We have provided an example to illustrate the significance of the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1532-:d:1394528
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    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. 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.
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