New oscillation criteria for third-order functional differential equations with general delay argument

Asma Al-Jaser; Inas Ibrhim; Faizah Alharbi; Belgees Qaraad; Dimplekumar Chalishajar; Asma Al-Jaser; Inas Ibrhim; Faizah Alharbi; Belgees Qaraad; Dimplekumar Chalishajar

doi:10.3934/math.20251288

AIMS Mathematics

2025, Volume 10, Issue 12: 29319-29341. doi: 10.3934/math.20251288

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New oscillation criteria for third-order functional differential equations with general delay argument

1.
Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Omar Al-Mukhtar University, Libya
3.
Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 24227, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
5.
Department of Applied Mathematics, Virginia Military Institute (VMI), Lexington, VA 24450, USA

Received: 12 October 2025 Revised: 22 November 2025 Accepted: 02 December 2025 Published: 12 December 2025
MSC : 34C10, 34K11

This study explores the asymptotic and oscillatory behavior of solutions to third-order functional differential equations. By employing Riccati transformation, we effectively eliminate the possibility of nonoscillatory solutions, allowing for the development of oscillation criteria that are applicable to a broad range of equation models. A key objective of this work is to relax traditional constraints commonly imposed on these criteria, thereby enhancing their general applicability. The results presented not only refine and extend existing theories but also contribute to a deeper understanding of the subject. Practical implications of the theoretical findings are demonstrated through several illustrative examples, highlighting their relevance and potential applications.
- functional differential equations,
- neutral term,
- oscillation,
- Riccati transformation
Citation: Asma Al-Jaser, Inas Ibrhim, Faizah Alharbi, Belgees Qaraad, Dimplekumar Chalishajar. New oscillation criteria for third-order functional differential equations with general delay argument[J]. AIMS Mathematics, 2025, 10(12): 29319-29341. doi: 10.3934/math.20251288

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Abstract

This study explores the asymptotic and oscillatory behavior of solutions to third-order functional differential equations. By employing Riccati transformation, we effectively eliminate the possibility of nonoscillatory solutions, allowing for the development of oscillation criteria that are applicable to a broad range of equation models. A key objective of this work is to relax traditional constraints commonly imposed on these criteria, thereby enhancing their general applicability. The results presented not only refine and extend existing theories but also contribute to a deeper understanding of the subject. Practical implications of the theoretical findings are demonstrated through several illustrative examples, highlighting their relevance and potential applications.

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