Second-order nonlinear neutral differential equations with delay term: Novel oscillation theorems

Saeed Althubiti; Saeed Althubiti

doi:10.3934/math.2025330

AIMS Mathematics

2025, Volume 10, Issue 3: 7223-7237. doi: 10.3934/math.2025330

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Research article

Second-order nonlinear neutral differential equations with delay term: Novel oscillation theorems

Saeed Althubiti ^,

Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 05 January 2025 Revised: 14 February 2025 Accepted: 20 February 2025 Published: 28 March 2025
MSC : 34C10, 34K11

This work aims to propose novel criteria to guarantee the oscillation of solutions for second-order differential equations. To analyze the oscillatory characteristics of the studied equation, new necessary conditions are introduced. We used a variety of analysis techniques to support these findings, forming fresh connections to tackle some issues that have impeded earlier studies. As a result, by using the Riccati transformation and the principles of comparison, we were able to acquire results that both expand upon and enhance those found in previous research. Several examples are presented to illustrate the significance of our findings.
- oscillation theorems,
- second-order,
- delay terms,
- differential equation
Citation: Saeed Althubiti. Second-order nonlinear neutral differential equations with delay term: Novel oscillation theorems[J]. AIMS Mathematics, 2025, 10(3): 7223-7237. doi: 10.3934/math.2025330

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Abstract

This work aims to propose novel criteria to guarantee the oscillation of solutions for second-order differential equations. To analyze the oscillatory characteristics of the studied equation, new necessary conditions are introduced. We used a variety of analysis techniques to support these findings, forming fresh connections to tackle some issues that have impeded earlier studies. As a result, by using the Riccati transformation and the principles of comparison, we were able to acquire results that both expand upon and enhance those found in previous research. Several examples are presented to illustrate the significance of our findings.

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