Second-order differential equations with mixed neutral terms: new oscillation theorems

Fawaz Khaled Alarfaj; Ali Muhib; Fawaz Khaled Alarfaj; Ali Muhib

doi:10.3934/math.2025156

AIMS Mathematics

2025, Volume 10, Issue 2: 3381-3391. doi: 10.3934/math.2025156

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Research article

Second-order differential equations with mixed neutral terms: new oscillation theorems

Fawaz Khaled Alarfaj ^{1
,
,},
Ali Muhib ^{2,3
,
,}

1.
Department of Management Information Systems, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
2.
Department of Mathematics, Faculty of Applied and Educational Sciences, Al-Nadera, Ibb University, Ibb, Yemen
3.
Jadara Research Center, Jadara University, Irbid 21110, Jordan

Received: 11 December 2024 Revised: 23 January 2025 Accepted: 08 February 2025 Published: 21 February 2025
MSC : 34C10, 34K11

Since differential equations play a major role in mathematics, physics, and engineering, the study of the oscillatory behavior of these equations is of great importance. In this paper, we apply the comparison method with first-order differential equations to study the oscillatory behavior of second-order differential equations. New oscillation criteria were obtained to improve some of the results of previous studies. Examples are included to illustrate the importance and novelty of the presented results.
- oscillation criteria,
- differential equations,
- non-canonical case,
- mixed neutral terms
Citation: Fawaz Khaled Alarfaj, Ali Muhib. Second-order differential equations with mixed neutral terms: new oscillation theorems[J]. AIMS Mathematics, 2025, 10(2): 3381-3391. doi: 10.3934/math.2025156

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Abstract

Since differential equations play a major role in mathematics, physics, and engineering, the study of the oscillatory behavior of these equations is of great importance. In this paper, we apply the comparison method with first-order differential equations to study the oscillatory behavior of second-order differential equations. New oscillation criteria were obtained to improve some of the results of previous studies. Examples are included to illustrate the importance and novelty of the presented results.

References

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