New criteria for the oscillation of a class of third-order quasilinear delay differential equations

Zuhur Alqahtani; Insaf F. Ben Saud; Areej Almuneef; Belgees Qaraad; Higinio Ramos; Zuhur Alqahtani; Insaf F. Ben Saud; Areej Almuneef; Belgees Qaraad; Higinio Ramos

doi:10.3934/math.2025195

AIMS Mathematics

2025, Volume 10, Issue 2: 4205-4225. doi: 10.3934/math.2025195

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Research article

New criteria for the oscillation of a class of third-order quasilinear delay differential equations

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, Faculty of Education, University of Benghazi, Benghazi, Libya
3.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
4.
Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
5.
Department of Mathematics, Escuela Politecnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain

Received: 15 December 2024 Revised: 05 February 2025 Accepted: 12 February 2025 Published: 27 February 2025
MSC : 34C10, 34K11

This paper establishes new criteria for the oscillation of solutions to a specific class of third-order delay differential equations. These equations, which have numerous applications in the physical and biological sciences, pose intriguing analytical challenges. By employing novel ordering properties, the comparison principle, Riccati transformations, and other analytical techniques, we derive effective oscillation criteria. This approach addresses and overcomes several restrictions previously imposed on the coefficients of such equations. To demonstrate the novelty and practical relevance of our results, we include illustrative examples.
- quasilinear differential equation,
- delay,
- third-order,
- oscillation
Citation: Zuhur Alqahtani, Insaf F. Ben Saud, Areej Almuneef, Belgees Qaraad, Higinio Ramos. New criteria for the oscillation of a class of third-order quasilinear delay differential equations[J]. AIMS Mathematics, 2025, 10(2): 4205-4225. doi: 10.3934/math.2025195

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Abstract

This paper establishes new criteria for the oscillation of solutions to a specific class of third-order delay differential equations. These equations, which have numerous applications in the physical and biological sciences, pose intriguing analytical challenges. By employing novel ordering properties, the comparison principle, Riccati transformations, and other analytical techniques, we derive effective oscillation criteria. This approach addresses and overcomes several restrictions previously imposed on the coefficients of such equations. To demonstrate the novelty and practical relevance of our results, we include illustrative examples.

References

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