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New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations

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  • Irena Jadlovská

    (Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovakia)

Abstract

In this paper, new oscillation criteria for second-order half-linear neutral delay differential equations are established, using a recently developed method of iteratively improved monotonicity properties of a nonoscillatory solution. Our approach allows removing several disadvantages which were commonly associated with the method based on a priori bound for the nonoscillatory solution, and deriving new results which are optimal in a nonneutral case. It is shown that the newly obtained results significantly improve a large number of existing ones.

Suggested Citation

  • Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2089-:d:624560
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    References listed on IDEAS

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    1. Candan, T., 2015. "Oscillatory behavior of second order nonlinear neutral differential equations with distributed deviating arguments," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 199-203.
    2. Agarwal, Ravi P. & Bohner, Martin & Li, Tongxing, 2015. "Oscillatory behavior of second-order half-linear damped dynamic equations," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 408-418.
    3. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, July.
    4. Chatzarakis, George E. & Grace, Said R. & Jadlovská, Irena, 2021. "On the sharp oscillation criteria for half-linear second-order differential equations with several delay arguments," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    5. 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.
    6. Deng, Xun-Huan & Wang, Qi-Ru & Zhou, Zhan, 2015. "Oscillation criteria for second order nonlinear delay dynamic equations on time scales," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 834-840.
    7. Omar Bazighifan & Clemente Cesarano, 2019. "Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
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    Cited by:

    1. Amany Nabih & Osama Moaaz & Sameh S. Askar & Ahmad M. Alshamrani & Elmetwally M. Elabbasy, 2023. "Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    2. 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.

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