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

Author

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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

    as
    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. 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. & 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.
    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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