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Oscillation Solutions for Nonlinear Second-Order Neutral Differential Equations

Author

Listed:
  • Omar Bazighifan

    (Department of Mathematics, Faculty of Science, Seiyun University, Hadhramout 50512, Yemen
    Jadara Research Center, 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)

  • Loredana Florentina Iambor

    (Department of Mathematics and Computer Science, University of Oradea, University Street, 410087 Oradea, Romania)

Abstract

This research investigates the oscillation criteria of nonlinear second-order neutral differential equations with multiple delays, focusing on their noncanonical forms. By leveraging an innovative iterative technique, new relationships are established to enhance the monotonic properties of positive solutions. These advancements lead to the derivation of novel oscillation criteria that significantly extend and refine the existing body of knowledge in this domain. The proposed criteria address gaps in the literature, providing a robust framework for analyzing such differential equations. To demonstrate their practical implications, three illustrative examples are presented, showcasing the applicability and effectiveness of the results in solving real-world problems involving delay differential equations.

Suggested Citation

  • Omar Bazighifan & Nawa Alshammari & Faten Aldosari & Loredana Florentina Iambor, 2025. "Oscillation Solutions for Nonlinear Second-Order Neutral Differential Equations," Mathematics, MDPI, vol. 13(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:247-:d:1566051
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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. Shyam Sundar Santra & Omar Bazighifan & Mihai Postolache, 2021. "New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms," Mathematics, MDPI, vol. 9(11), pages 1-9, May.
    3. Shurong Sun & Tongxing Li & Zhenlai Han & Hua Li, 2012. "Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, July.
    Full references (including those not matched with items on IDEAS)

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