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Equivalence Transformation for Neutral Differential Equations: Oscillation of Solutions

Author

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  • Ağacık Zafer

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Tuncay Candan

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

  • Zeynep Nilhan Gürkan

    (College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait)

Abstract

We introduce an equivalence transformation to study the oscillation behavior of solutions for linear neutral differential equations of canonical and noncanonical types. The new approach leads to several novel oscillation criteria. Moreover, we show that the same arguments can be applied to nonlinear neutral equations under suitable monotonicity conditions. The importance of the results is also supported by examples.

Suggested Citation

  • Ağacık Zafer & Tuncay Candan & Zeynep Nilhan Gürkan, 2025. "Equivalence Transformation for Neutral Differential Equations: Oscillation of Solutions," Mathematics, MDPI, vol. 13(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2243-:d:1699159
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    References listed on IDEAS

    as
    1. 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.
    2. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, July.
    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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