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Topological structure of the solution set for a Volterra-type nonautonomous evolution inclusion with impulsive effect

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Abstract

This paper is devoted to study the topological structure of solution sets for a Volterra-type nonautonomous evolution inclusion with impulsive effects in a Fréchet space. The evolution family generated by the operator in the principal part is of no equicontinuity. Our attention is paid to establish the \(R_\delta \)-structure of the solution set and geometric features of the corresponding solution map. Moreover, the long-time existence of the nonlocal Cauchy problem is also considered. Finally, we present an example to illustrate the applicability of our abstract results.

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Acknowledgements

The authors want to express their thanks to the anonymous referees for their suggestions and comments that improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, People’s Republic of China

    Zhong-Xin Ma

  2. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Zhong-Xin Ma

  3. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, 221018, People’s Republic of China

    Yang-Yang Yu

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  1. Zhong-Xin Ma
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  2. Yang-Yang Yu
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All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

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Correspondence to Yang-Yang Yu.

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The research leading to the results of this paper has received funding from the NSFC (No. 11971317) and the scientific research start funds for Xuzhou University of Technology advanced talents introduction (No. 02900264)

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Ma, ZX., Yu, YY. Topological structure of the solution set for a Volterra-type nonautonomous evolution inclusion with impulsive effect. Z. Angew. Math. Phys. 73, 162 (2022). https://doi.org/10.1007/s00033-022-01810-z

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  • DOI: https://doi.org/10.1007/s00033-022-01810-z

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