Existence of solutions of an impulsive integro-differential equation with a general boundary value condition

Bing Hu; Minbo Xu; Zhizhi Wang; Jiahui Lin; Luyao Zhu; Dingjiang Wang; Bing Hu; Minbo Xu; Zhizhi Wang; Jiahui Lin; Luyao Zhu; Dingjiang Wang

doi:10.3934/mbe.2022192

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 4166-4177. doi: 10.3934/mbe.2022192

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Existence of solutions of an impulsive integro-differential equation with a general boundary value condition

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

Academic Editor: E. Oterkus

Received: 17 November 2021 Revised: 14 January 2022 Accepted: 20 January 2022 Published: 17 February 2022

In this paper, we discuss the existence of solutions for a first-order nonlinear impulsive integro-differential equation with a general boundary value condition. New comparison principles are developed, and existence results for extremal solutions are obtained using the established principles and the monotone iterative technique. The results are more general than those of the periodic boundary problems, which may be widely applied in this field.
- impulsive integro-differential equation,
- boundary value condition,
- comparison result,
- minimal and maximal solutions
Citation: Bing Hu, Minbo Xu, Zhizhi Wang, Jiahui Lin, Luyao Zhu, Dingjiang Wang. Existence of solutions of an impulsive integro-differential equation with a general boundary value condition[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 4166-4177. doi: 10.3934/mbe.2022192

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Abstract

In this paper, we discuss the existence of solutions for a first-order nonlinear impulsive integro-differential equation with a general boundary value condition. New comparison principles are developed, and existence results for extremal solutions are obtained using the established principles and the monotone iterative technique. The results are more general than those of the periodic boundary problems, which may be widely applied in this field.

References

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