Noncanonical second-order differential equations with several time-delay arguments: Enhancing oscillation criteria

A. Essam; A. Al-Jaser; S. R. Grace; H. Ramos; O. Moaaz; A. Essam; A. Al-Jaser; S. R. Grace; H. Ramos; O. Moaaz

doi:10.3934/era.2026178

Electronic Research Archive

2026, Volume 34, Issue 6: 3968-3990. doi: 10.3934/era.2026178

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Noncanonical second-order differential equations with several time-delay arguments: Enhancing oscillation criteria

1.
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt
4.
Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
5.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt

Received: 24 January 2026 Revised: 28 March 2026 Accepted: 14 April 2026 Published: 14 May 2026

This study investigates the oscillatory properties of solutions for a general class of neutral differential equations with multiple delays. Using Riccati and comparison techniques, we establish five distinct oscillation theorems that address the limitations of previous results in this topic. Our criteria not only extend and generalize earlier findings but also reduce the required constraints. Notably, they provide sharper results when applied to special cases like Euler's equation. The novelty and effectiveness of the proposed oscillation criteria are illustrated through a detailed analysis of a given example, supported by tables and figures.
- differential equations,
- oscillatory properties,
- Riccati and comparison techniques,
- noncanonical second-order,
- several time-delay arguments
Citation: A. Essam, A. Al-Jaser, S. R. Grace, H. Ramos, O. Moaaz. Noncanonical second-order differential equations with several time-delay arguments: Enhancing oscillation criteria[J]. Electronic Research Archive, 2026, 34(6): 3968-3990. doi: 10.3934/era.2026178

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Abstract

This study investigates the oscillatory properties of solutions for a general class of neutral differential equations with multiple delays. Using Riccati and comparison techniques, we establish five distinct oscillation theorems that address the limitations of previous results in this topic. Our criteria not only extend and generalize earlier findings but also reduce the required constraints. Notably, they provide sharper results when applied to special cases like Euler's equation. The novelty and effectiveness of the proposed oscillation criteria are illustrated through a detailed analysis of a given example, supported by tables and figures.

References

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