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An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type

Author

Listed:
  • Osama Moaaz

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

  • Ali Muhib

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, Faculty of Education—Al-Nadirah, Ibb University, Ibb 70270, Yemen)

  • Shyam S. Santra

    (Department of Mathematics, JIS College of Engineering, Kalyani 741235, India)

Abstract

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations.

Suggested Citation

  • Osama Moaaz & Ali Muhib & Shyam S. Santra, 2021. "An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1634-:d:592167
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    References listed on IDEAS

    as
    1. 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.
    2. Jozef Džurina & Said R. Grace & Irena Jadlovská & Tongxing Li, 2020. "Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 910-922, May.
    3. Omar Bazighifan, 2020. "Some New Oscillation Results for Fourth-Order Neutral Differential Equations with a Canonical Operator," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, October.
    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.
    5. Siyu Zhang & Fanwei Meng, 2010. "Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-14, January.
    Full references (including those not matched with items on IDEAS)

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