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AIMS Mathematics

2025, Volume 10, Issue 12: 29607-29626. doi: 10.3934/math.20251301
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Research article

Novel oscillation criteria for general third-order nonlinear neutral differential equations

  • 1.
    Department of Mathematics, University of Saba Region, Marib, Yemen
  • 2.
    Department of Mathematics, Faculty of Science, University of Hafr Al Batin, P.O. Box 1803, Hafar Al Batin 31991, Saudi Arabia
  • 3.
    Department of Mathematics and Computer Science, University of Oradea, University Street, Oradea 410087, Romania
  • 4.
    Science and Mathematics Unit, University of Technology and Applied Sciences, P.O. Box 466, Ibri 516, Oman
  • 5.
    Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen
  • 6.
    Jadara Research Center, Jadara University, Irbid 21110, Jordan
  • Published: 15 December 2025

  • MSC : 34C10, 34K11

  • This research aims to introduce new criteria that guarantee the oscillation of all solutions to third-order nonlinear neutral differential equations in their canonical form. The proposed methodology integrates the comparison principle with first-order differential equations and employs the Riccati substitution technique, which simplifies the complex structure of the equations and transforms them into more analyzable forms. This approach contributes to establishing general and precise oscillation conditions, representing an extension and improvement over previously published work in this field. It is important to note that this study is purely analytical, focusing on the derivation of oscillatory properties and theoretical criteria. To validate the applicability of the results, three numerical examples are provided, demonstrating the capability of the proposed criteria to verify the oscillation of solutions and highlighting both the theoretical and practical significance of the methodology.

    Citation: Fahd Masood, Alanoud Almutairi, Loredana Florentina Iambor, Khalil S. Al-Ghafri, Omar Bazighifan. Novel oscillation criteria for general third-order nonlinear neutral differential equations[J]. AIMS Mathematics, 2025, 10(12): 29607-29626. doi: 10.3934/math.20251301

    Related Papers:

  • This research aims to introduce new criteria that guarantee the oscillation of all solutions to third-order nonlinear neutral differential equations in their canonical form. The proposed methodology integrates the comparison principle with first-order differential equations and employs the Riccati substitution technique, which simplifies the complex structure of the equations and transforms them into more analyzable forms. This approach contributes to establishing general and precise oscillation conditions, representing an extension and improvement over previously published work in this field. It is important to note that this study is purely analytical, focusing on the derivation of oscillatory properties and theoretical criteria. To validate the applicability of the results, three numerical examples are provided, demonstrating the capability of the proposed criteria to verify the oscillation of solutions and highlighting both the theoretical and practical significance of the methodology.



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  • © 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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