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Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order

Author

Listed:
  • Taher S. Hassan

    (Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Qingkai Kong

    (Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA)

  • Bassant M. El-Matary

    (Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 51951, Saudi Arabia
    Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt)

Abstract

In this paper, we find new oscillation criteria for second-order advanced functional half-linear differential equations. Our results extend and improve recent criteria for the same equations established previously by several authors and cover the existing classical criteria for related ordinary differential equations. We give some examples to illustrate the significance of the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1385-:d:1095649
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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. Quanxin Zhang & Xia Song, 2014. "On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, April.
    3. 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.
    4. Blanka Baculikova, 2021. "Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments," Mathematics, MDPI, vol. 9(20), pages 1-12, October.
    5. 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.
    6. Shouhua Liu & Quanxin Zhang, 2014. "New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, June.
    7. 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)

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    Cited by:

    1. Yingying Wang & Zhinan Xia, 2023. "Lipschitz Stability in Terms of Two Measures for Kurzweil Equations and Applications," Mathematics, MDPI, vol. 11(9), pages 1-20, April.
    2. 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.
    3. Hail S. Alrashdi & Osama Moaaz & Khaled Alqawasmi & Mohammad Kanan & Mohammed Zakarya & Elmetwally M. Elabbasy, 2024. "Asymptotic and Oscillatory Properties of Third-Order Differential Equations with Multiple Delays in the Noncanonical Case," Mathematics, MDPI, vol. 12(8), pages 1-15, April.

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