Nonlinear neutral differential equations of second-order: Oscillatory properties

Maged Alkilayh; Maged Alkilayh

doi:10.3934/math.2025073

AIMS Mathematics

2025, Volume 10, Issue 1: 1589-1601. doi: 10.3934/math.2025073

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Nonlinear neutral differential equations of second-order: Oscillatory properties

Maged Alkilayh ^,

Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Received: 24 September 2024 Revised: 02 December 2024 Accepted: 16 December 2024 Published: 23 January 2025
MSC : 34C10, 34K11

This paper investigates the oscillatory behavior of second-order differential equations featuring a mixed neutral term along with a $ p $-Laplace differential operator. The analysis employs Riccati transformations and includes a comparative study with first-order equations, which facilitates the development of oscillation criteria. The findings culminate in a significant theorem that addresses the oscillation properties of these equations. In addition, two illustrative examples are presented to demonstrate the practical application of the established criteria.
- mixed neutral,
- differential equations,
- oscillation conditions,
- second-order
Citation: Maged Alkilayh. Nonlinear neutral differential equations of second-order: Oscillatory properties[J]. AIMS Mathematics, 2025, 10(1): 1589-1601. doi: 10.3934/math.2025073

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Abstract

This paper investigates the oscillatory behavior of second-order differential equations featuring a mixed neutral term along with a $ p $-Laplace differential operator. The analysis employs Riccati transformations and includes a comparative study with first-order equations, which facilitates the development of oscillation criteria. The findings culminate in a significant theorem that addresses the oscillation properties of these equations. In addition, two illustrative examples are presented to demonstrate the practical application of the established criteria.

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