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Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior

Author

Listed:
  • Belal Batiha

    (Mathematics Department, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan)

  • Nawa Alshammari

    (Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia)

  • Faten Aldosari

    (Department of Mathematics, College of Science, Shaqra University, P.O. Box 15572, Shaqra 11961, Saudi Arabia)

  • Fahd Masood

    (Department of Mathematics, Faculty of Education and Science, University of Saba Region, Marib 14400, Yemen)

  • Omar Bazighifan

    (Department of Mathematics, Faculty of Education, Seiyun University, Seiyun 50512, Yemen
    Jadara Research Center, Jadara University, Irbid 21110, Jordan)

Abstract

This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of solutions and their derivatives, paving the way for a deeper understanding of this complex behavior. The research is particularly significant as it extends the scope of previous studies by addressing more complex forms of neutral differential equations. Using the linearization technique, strict conditions are developed that exclude the existence of positive solutions, which allows the formulation of innovative criteria for determining the oscillatory behavior of the studied equations. This research highlights the theoretical and applied aspects of this mathematical phenomenon, which contributes to enhancing the scientific understanding of differential equations with neutral conditions. To demonstrate the effectiveness of the results, the research includes two illustrative examples that prove the validity and importance of the proposed methodology. This work represents a qualitative addition to the mathematical literature, as it lays new foundations and opens horizons for future studies in this vital field.

Suggested Citation

  • Belal Batiha & Nawa Alshammari & Faten Aldosari & Fahd Masood & Omar Bazighifan, 2025. "Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior," Mathematics, MDPI, vol. 13(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:147-:d:1559004
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    References listed on IDEAS

    as
    1. Bazighifan, Omar, 2020. "On the oscillation of certain fourth-order differential equations with p-Laplacian like operator," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. 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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