Study on the oscillation of solution to second-order impulsive systems

Shyam Sundar Santra; Palash Mondal; Mohammad Esmael Samei; Hammad Alotaibi; Mohamed Altanji; Thongchai Botmart; Shyam Sundar Santra; Palash Mondal; Mohammad Esmael Samei; Hammad Alotaibi; Mohamed Altanji; Thongchai Botmart

doi:10.3934/math.20231134

AIMS Mathematics

2023, Volume 8, Issue 9: 22237-22255. doi: 10.3934/math.20231134

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Research article

Study on the oscillation of solution to second-order impulsive systems

1.
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India
2.
Assistant Teacher of Sankarpur High Madrasah (HS), Murshidabad 742159, India
3.
Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178-38695, Iran
4.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
5.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 02 September 2022 Revised: 29 December 2022 Accepted: 09 January 2023 Published: 13 July 2023
MSC : 34C10, 34C15, 34K11

In the present article, we set the if and only if conditions for the solutions of the class of neutral impulsive delay second-order differential equations. We consider two cases when it is non-increasing and non-decreasing for quotient of two positive odd integers. Our main tool is the Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.
- nonlinear,
- nonoscillation,
- delay argument,
- second-order differential equation,
- Lebesgue's dominated convergence theorem
Citation: Shyam Sundar Santra, Palash Mondal, Mohammad Esmael Samei, Hammad Alotaibi, Mohamed Altanji, Thongchai Botmart. Study on the oscillation of solution to second-order impulsive systems[J]. AIMS Mathematics, 2023, 8(9): 22237-22255. doi: 10.3934/math.20231134

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Abstract

In the present article, we set the if and only if conditions for the solutions of the class of neutral impulsive delay second-order differential equations. We consider two cases when it is non-increasing and non-decreasing for quotient of two positive odd integers. Our main tool is the Lebesgue's dominated convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.

References

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