New oscillation results for noncanonical quasilinear differential equations of neutral type

Hail S. Alrashdi; Fahd Masood; Ahmad M. Alshamrani; Sameh S. Askar; Monica Botros; Hail S. Alrashdi; Fahd Masood; Ahmad M. Alshamrani; Sameh S. Askar; Monica Botros

doi:10.3934/math.2025647

AIMS Mathematics

2025, Volume 10, Issue 6: 14372-14391. doi: 10.3934/math.2025647

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Research article

New oscillation results for noncanonical quasilinear differential equations of neutral type

1.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
2.
Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia
3.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy

Received: 05 December 2024 Revised: 09 February 2025 Accepted: 25 February 2025 Published: 23 June 2025
MSC : 34C10, 34K11

This article explored oscillation conditions for quasi-linear neutral differential equations of noncanonical form. By establishing new iterative monotonic properties of solutions, we derived novel oscillation criteria that extend and refine existing results in the literature. To illustrate the significance of our findings, we provided three concrete examples demonstrating the applicability of the proposed conditions.
- oscillatory,
- nonoscillatory,
- neutral differential equations,
- second-order,
- noncanonical
Citation: Hail S. Alrashdi, Fahd Masood, Ahmad M. Alshamrani, Sameh S. Askar, Monica Botros. New oscillation results for noncanonical quasilinear differential equations of neutral type[J]. AIMS Mathematics, 2025, 10(6): 14372-14391. doi: 10.3934/math.2025647

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Abstract

This article explored oscillation conditions for quasi-linear neutral differential equations of noncanonical form. By establishing new iterative monotonic properties of solutions, we derived novel oscillation criteria that extend and refine existing results in the literature. To illustrate the significance of our findings, we provided three concrete examples demonstrating the applicability of the proposed conditions.

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