Controllability of nonlinear ordinary differential equations with non-instantaneous impulses

Zhen Xin; Yuhe Yang; Qiaoxia Li; Zhen Xin; Yuhe Yang; Qiaoxia Li

doi:10.3934/mmc.2022001

Mathematical Modelling and Control

2022, Volume 2, Issue 1: 1-6. doi: 10.3934/mmc.2022001

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Research article

Controllability of nonlinear ordinary differential equations with non-instantaneous impulses

1.
School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
2.
Institute of Applied Mathematics, Yili Normal University, Yining 835000, China

Received: 04 October 2021 Revised: 31 December 2021 Accepted: 15 January 2022 Published: 19 January 2022

In this paper, we consider controllability of the initial value problem with non-instantaneous impulse on ordered Banach spaces. We firstly give a solution expression for initial value problems with non-instantaneous impulses in ordered Banach Spaces by using Schauder fixed point theorem. Sufficient conditions for controllability results are obtained by Krasnoselskii's fixed point theorem in the infinite-dimensional spaces. An example is also given to illustrate the feasibility of our theoretical results.
- non-instantaneous impulses,
- controllability,
- Banach spaces
Citation: Zhen Xin, Yuhe Yang, Qiaoxia Li. Controllability of nonlinear ordinary differential equations with non-instantaneous impulses[J]. Mathematical Modelling and Control, 2022, 2(1): 1-6. doi: 10.3934/mmc.2022001

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Abstract

In this paper, we consider controllability of the initial value problem with non-instantaneous impulse on ordered Banach spaces. We firstly give a solution expression for initial value problems with non-instantaneous impulses in ordered Banach Spaces by using Schauder fixed point theorem. Sufficient conditions for controllability results are obtained by Krasnoselskii's fixed point theorem in the infinite-dimensional spaces. An example is also given to illustrate the feasibility of our theoretical results.

References

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