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Research Article | Open Access

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

Shyam Sundar Santra1, Palash Mondal2, Mohammad Esmael Samei3, Hammad Alotaibi4, Mohamed Altanji5, Thongchai Botmart6( )
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India
Assistant Teacher of Sankarpur High Madrasah (HS), Murshidabad 742159, India
Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178-38695, Iran
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
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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.

Keywords

nonlinearnonoscillationdelay argumentsecond-order differential equationLebesgue's dominated convergence theorem
CLC number: 34C10, 34C15, 34K11

References

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 22237-22255
DOI: 10.3934/math.20231134

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Cite this article:
Santra SS, Mondal P, Samei ME, et al. Study on the oscillation of solution to second-order impulsive systems. AIMS Mathematics, 2023, 8(9): 22237-22255. https://doi.org/10.3934/math.20231134

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Received: 02 September 2022
Revised: 29 December 2022
Accepted: 09 January 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)