Oscillation theorems for fourth-order quasi-linear delay differential equations

Fahd Masood; Osama Moaaz; Shyam Sundar Santra; U. Fernandez-Gamiz; Hamdy A. El-Metwally; Fahd Masood; Osama Moaaz; Shyam Sundar Santra; U. Fernandez-Gamiz; Hamdy A. El-Metwally

doi:10.3934/math.2023834

AIMS Mathematics

2023, Volume 8, Issue 7: 16291-16307. doi: 10.3934/math.2023834

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Research article

Oscillation theorems for fourth-order quasi-linear delay differential equations

1.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
2.
Department of mathematics, Faculty of Education and science, University of Saba Region, Marib, Yemen
3.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
4.
Department of Mathematics, JIS College of Engineering, Kalyani, Nadia, West Bengal 741235, India
5.
Department of Mathematics, Applied Science Cluster, University of Petroleum and Energy Studies (UPES), Dehradun, Uttarakhand 248007, India
6.
Nuclear Engineering and Fluid Mechanics Department, University of the Basque Country UPV/EHU, Vitoria-Gasteiz, Spain

Received: 14 December 2022 Revised: 12 March 2023 Accepted: 20 March 2023 Published: 08 May 2023
MSC : 34C10, 34K11

In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, $ \mathcal{N}_{a} $. As an extension of the approach taken in ^[1], we establish a new criterion that guarantees that $ \mathcal{N}_{a} = \emptyset $. Then, we create a new oscillation criterion.
- oscillatory behavior,
- nonoscillatory behavior,
- delay differential equation,
- fourth order
Citation: Fahd Masood, Osama Moaaz, Shyam Sundar Santra, U. Fernandez-Gamiz, Hamdy A. El-Metwally. Oscillation theorems for fourth-order quasi-linear delay differential equations[J]. AIMS Mathematics, 2023, 8(7): 16291-16307. doi: 10.3934/math.2023834

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Abstract

In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, $ \mathcal{N}_{a} $. As an extension of the approach taken in ^[1], we establish a new criterion that guarantees that $ \mathcal{N}_{a} = \emptyset $. Then, we create a new oscillation criterion.

References

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