Monotone iterative and quasilinearization method for a nonlinear integral impulsive differential equation

Yan Li; Zihan Rui; Bing Hu; Yan Li; Zihan Rui; Bing Hu

doi:10.3934/math.2025002

AIMS Mathematics

2025, Volume 10, Issue 1: 21-37. doi: 10.3934/math.2025002

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Research article Topical Sections

Monotone iterative and quasilinearization method for a nonlinear integral impulsive differential equation

School of Mathematical Sciences, Zhejiang University of Technology, Hangzhou 310023, China

Received: 06 October 2024 Revised: 09 December 2024 Accepted: 23 December 2024 Published: 02 January 2025
MSC : 34B05, 34B37

In this paper, we discuss the existence and approximation of solution sequences for a class of nonlinear ordinary differential equations with an impulsive integral condition. Our major methods were the monotone iterative and quasilinearization techniques. Interestingly, many new results could be obtained, which were different from the functional differential equation.
- impulsive integral condition,
- monotone iterative technique,
- quasilinearization method,
- quadratic convergence
Citation: Yan Li, Zihan Rui, Bing Hu. Monotone iterative and quasilinearization method for a nonlinear integral impulsive differential equation[J]. AIMS Mathematics, 2025, 10(1): 21-37. doi: 10.3934/math.2025002

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Abstract

In this paper, we discuss the existence and approximation of solution sequences for a class of nonlinear ordinary differential equations with an impulsive integral condition. Our major methods were the monotone iterative and quasilinearization techniques. Interestingly, many new results could be obtained, which were different from the functional differential equation.

References

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