Total controllability of non-autonomous second-order measure evolution systems with state-dependent delay and non-instantaneous impulses

Yang Wang; Yongyang Liu; Yansheng Liu; Yang Wang; Yongyang Liu; Yansheng Liu

doi:10.3934/mbe.2023095

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 2061-2080. doi: 10.3934/mbe.2023095

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Total controllability of non-autonomous second-order measure evolution systems with state-dependent delay and non-instantaneous impulses

1.
School of Information Engineering, Shandong Management University, Jinan 250357, China
2.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Received: 19 September 2022 Revised: 06 November 2022 Accepted: 09 November 2022 Published: 14 November 2022

This paper investigates a new class of non-autonomous second-order measure evolution systems involving state-dependent delay and non-instantaneous impulses. We introduce a stronger concept of exact controllability called total controllability. The existence of mild solutions and controllability for the considered system are obtained by applying strongly continuous cosine family and the Mönch fixed point theorem. Finally, an example is used to verify the practical application of the conclusion.
- Mönch fixed point theorem,
- second-order evolution systems,
- state-dependent delay,
- non-instantaneous impulses,
- total controllability
Citation: Yang Wang, Yongyang Liu, Yansheng Liu. Total controllability of non-autonomous second-order measure evolution systems with state-dependent delay and non-instantaneous impulses[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 2061-2080. doi: 10.3934/mbe.2023095

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Abstract

This paper investigates a new class of non-autonomous second-order measure evolution systems involving state-dependent delay and non-instantaneous impulses. We introduce a stronger concept of exact controllability called total controllability. The existence of mild solutions and controllability for the considered system are obtained by applying strongly continuous cosine family and the Mönch fixed point theorem. Finally, an example is used to verify the practical application of the conclusion.

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