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Asymptotic and Oscillatory Analysis of Second-Order Differential Equations with Distributed Deviating Arguments

Author

Listed:
  • Zuhur Alqahtani

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

  • Belgees Qaraad

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

  • Areej Almuneef

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

  • Higinio Ramos

    (Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
    Department of Mathematics, Escuela Politecnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain)

Abstract

This paper focuses on studying the oscillatory properties of a distinctive class of second-order advanced differential equations with distributed deviating arguments in a noncanonical case. Utilizing the Riccati method and the comparison method with first-order equations, in addition to other analytical methods, we have established criteria to test whether the solutions of the studied equation exhibit oscillatory behavior. To verify the validity of the results we obtained and determine their applicability, we present some examples to confirm the strength and accuracy of our proposed criteria.

Suggested Citation

  • Zuhur Alqahtani & Belgees Qaraad & Areej Almuneef & Higinio Ramos, 2024. "Asymptotic and Oscillatory Analysis of Second-Order Differential Equations with Distributed Deviating Arguments," Mathematics, MDPI, vol. 12(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3542-:d:1519770
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    References listed on IDEAS

    as
    1. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, July.
    2. Agarwal, Ravi P. & Bohner, Martin & Li, Tongxing & Zhang, Chenghui, 2015. "Even-order half-linear advanced differential equations: improved criteria in oscillatory and asymptotic properties," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 481-490.
    3. Alanoud Almutairi & Ali Hasan Ali & Omar Bazighifan & Loredana Florentina Iambor, 2023. "Oscillatory Properties of Fourth-Order Advanced Differential Equations," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    4. Agarwal, Ravi P. & Zhang, Chenghui & Li, Tongxing, 2016. "Some remarks on oscillation of second order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 178-181.
    Full references (including those not matched with items on IDEAS)

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