On the oscillation of solutions of third-order differential equations with non-positive neutral coefficients

A. A. El-Gaber; M. M. A. El-Sheikh; M. Zakarya; Amirah Ayidh I Al-Thaqfan; H. M. Rezk; A. A. El-Gaber; M. M. A. El-Sheikh; M. Zakarya; Amirah Ayidh I Al-Thaqfan; H. M. Rezk

doi:10.3934/math.20241548

AIMS Mathematics

2024, Volume 9, Issue 11: 32257-32271. doi: 10.3934/math.20241548

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On the oscillation of solutions of third-order differential equations with non-positive neutral coefficients

1.
Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt
2.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
3.
Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Sarat Ubaidah, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt

Received: 03 September 2024 Revised: 20 October 2024 Accepted: 30 October 2024 Published: 14 November 2024
MSC : 34C10, 34K11

The oscillation property of third-order differential equations with non-positive neutral coefficients is discussed. New sufficient conditions are provided to guarantee that every solution of the considered equation is almost oscillatory. Both the canonical and non-canonical cases are considered. Illustrative examples are introduced to support the obtained results.
- oscillation,
- third-order,
- nonpositive neutral coefficients
Citation: A. A. El-Gaber, M. M. A. El-Sheikh, M. Zakarya, Amirah Ayidh I Al-Thaqfan, H. M. Rezk. On the oscillation of solutions of third-order differential equations with non-positive neutral coefficients[J]. AIMS Mathematics, 2024, 9(11): 32257-32271. doi: 10.3934/math.20241548

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Abstract

The oscillation property of third-order differential equations with non-positive neutral coefficients is discussed. New sufficient conditions are provided to guarantee that every solution of the considered equation is almost oscillatory. Both the canonical and non-canonical cases are considered. Illustrative examples are introduced to support the obtained results.

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