On the oscillation of fourth-order canonical differential equation with several delays

Mohammed Ahmed Alomair; Ali Muhib; Mohammed Ahmed Alomair; Ali Muhib

doi:10.3934/math.2024975

AIMS Mathematics

2024, Volume 9, Issue 8: 19997-20013. doi: 10.3934/math.2024975

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Research article

On the oscillation of fourth-order canonical differential equation with several delays

Mohammed Ahmed Alomair ^{1
,
,},
Ali Muhib ^{2,3
,
,}

1.
Department of Quantitative Methods, 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.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 22 April 2024 Revised: 11 June 2024 Accepted: 13 June 2024 Published: 20 June 2024
MSC : 34C10, 34K11

This study is concerned with investigating the oscillatory properties of a general class of neutral differential equations. Neutral equations are characterized by being rich in both practical and theoretical aspects. We obtain criteria that guarantee the oscillation of solutions to a fourth-order neutral differential equation with multiple delays. Considering the canonical case, we obtain some new relations and inequalities that help in obtaining improved criteria. We use the reduction method to relate the oscillation of the studied equation to a first-order equation. We apply the results to a special case. Through this application, we evaluated the efficiency of the new results in the oscillation test compared to previous results in the literature.
- canonical form,
- fourth-order,
- oscillation criteria
Citation: Mohammed Ahmed Alomair, Ali Muhib. On the oscillation of fourth-order canonical differential equation with several delays[J]. AIMS Mathematics, 2024, 9(8): 19997-20013. doi: 10.3934/math.2024975

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Abstract

This study is concerned with investigating the oscillatory properties of a general class of neutral differential equations. Neutral equations are characterized by being rich in both practical and theoretical aspects. We obtain criteria that guarantee the oscillation of solutions to a fourth-order neutral differential equation with multiple delays. Considering the canonical case, we obtain some new relations and inequalities that help in obtaining improved criteria. We use the reduction method to relate the oscillation of the studied equation to a first-order equation. We apply the results to a special case. Through this application, we evaluated the efficiency of the new results in the oscillation test compared to previous results in the literature.

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