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Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

Author

Listed:
  • Hail S. Alrashdi

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Wedad Albalawi

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Ali Muhib

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Osama Moaaz

    (Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia)

  • Elmetwally M. Elabbasy

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

This paper aims to study the asymptotic properties of nonoscillatory solutions (eventually positive or negative) of a class of third-order canonical neutral differential equations. We use Riccati substitution to reduce the order of the considered equation, and then we use the Philos function class to obtain new criteria of the Kamenev type, which guarantees that all nonoscillatory solutions converge to zero. This approach is characterized by the possibility of applying its conditions to a wider area of equations. This is not the only aspect that distinguishes our results; we also use improved relationships between the solution and the corresponding function, which in turn is reflected in a direct improvement of the criteria. The findings in this article extend and generalize previous findings in the literature and also improve some of these findings.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1734-:d:1407586
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    References listed on IDEAS

    as
    1. 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.
    2. Osama Moaaz & Yousef Alnafisah, 2023. "An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    3. Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    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. Osama Moaaz & Jan Awrejcewicz & Ali Muhib, 2020. "Establishing New Criteria for Oscillation of Odd-Order Nonlinear Differential Equations," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    6. Jadlovská, Irena & Džurina, Jozef, 2020. "Kneser-type oscillation criteria for second-order half-linear delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 380(C).
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