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Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior

Author

Listed:
  • Asma Al-Jaser

    (Department of Mathematical Science, 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)

  • Omar Bazighifan

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

  • Loredana Florentina Iambor

    (Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania)

Abstract

In this paper, new criteria for a class oscillation of second-order delay differential equations with distributed deviating arguments were established. Our method mainly depends on making sharper estimates for the non-oscillatory solutions of the studied equation. By using the Ricati technique and comparison theorems that compare the studied equations with first-order delay differential equations, we obtained new and less restrictive conditions that ensure the oscillation of all solutions of the studied equation. Further, we give an illustrative example.

Suggested Citation

  • Asma Al-Jaser & Belgees Qaraad & Omar Bazighifan & Loredana Florentina Iambor, 2023. "Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2605-:d:1165856
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    References listed on IDEAS

    as
    1. Omar Bazighifan & Poom Kumam, 2020. "Oscillation Theorems for Advanced Differential Equations with p -Laplacian Like Operators," Mathematics, MDPI, vol. 8(5), pages 1-10, May.
    2. Barakah Almarri & Ali Hasan Ali & António M. Lopes & Omar Bazighifan, 2022. "Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions," Mathematics, MDPI, vol. 10(6), pages 1-10, March.
    3. 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.
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    Cited by:

    1. Munirah Aldiaiji & Belgees Qaraad & Loredana Florentina Iambor & Safi S. Rabie & Elmetwally M. Elabbasy, 2023. "Oscillation of Third-Order Differential Equations with Advanced Arguments," Mathematics, MDPI, vol. 12(1), pages 1-12, December.
    2. Abdulaziz Khalid Alsharidi & Ali Muhib & Sayed K. Elagan, 2023. "Neutral Differential Equations of Higher-Order in Canonical Form: Oscillation Criteria," Mathematics, MDPI, vol. 11(15), pages 1-13, July.

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