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Existence for Semilinear Impulsive Differential Inclusions Without Compactness

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Abstract

In this paper, we establish sufficient conditions on the existence of mild solutions for semilinear impulsive differential inclusions by using Glicksberg-Ky Fan fixed point theorem with weak topology technique. We do not require the compactness of the evolution operator generated by the linear part and of the multivalued nonlinear term. An example is also presented.

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Acknowledgements

The author is grateful to the referees for their valuable comments and suggestions.

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  1. School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan, 411201, China

    Yan Luo

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  1. Yan Luo
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Correspondence to Yan Luo.

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Luo, Y. Existence for Semilinear Impulsive Differential Inclusions Without Compactness. J Dyn Control Syst 26, 663–672 (2020). https://doi.org/10.1007/s10883-019-09473-2

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  • DOI: https://doi.org/10.1007/s10883-019-09473-2

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