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Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation

Author

Listed:
  • Osama Moaaz
  • Ali Muhib
  • Saud Owyed
  • Emad E. Mahmoud
  • Aml Abdelnaser
  • Kottakkaran Sooppy Nisar

Abstract

The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation rlu′lγ′+qlxβσl=0, where l≥l0 and ul≔xl+pxϱl. By optimizing the commonly used relationship x>1−pu, we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.

Suggested Citation

  • Osama Moaaz & Ali Muhib & Saud Owyed & Emad E. Mahmoud & Aml Abdelnaser & Kottakkaran Sooppy Nisar, 2021. "Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, February.
    • Handle: RePEc:hin:jjmath:6665103
    DOI: 10.1155/2021/6665103
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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. Osama Moaaz & Clemente Cesarano & Barakah Almarri, 2023. "An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications," Mathematics, MDPI, vol. 11(7), pages 1-14, April.

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