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Periodic Boundary Value Problem for Impulsive Evolution Equations with Noncompact Semigroup

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Abstract

In this paper, by applying the Sadovskii’s fixed point theorem, we obtain the existence and uniqueness result of mild solution for a class of periodic boundary value problem of impulsive evolution equations in Banach space with noncompact semigroup in the case that the nonlinearity term f and impulsive functions \(I_k\) satisfy growth conditions and the measure of noncompactness conditions. And we give a specific example to illustrate our main results.

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Funding

Funding was provided by the National Natural Science Foundation of China (Nos. 12061062, 11661071) and 2022 Gansu Province Excellent Graduate Student “Innovation Star” Project (2022CXZX-240).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Weifeng Ma & Yongxiang Li

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  1. Weifeng Ma
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  2. Yongxiang Li
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Contributions

WM completed the proof of the main results and the writing of the first draft. YL revised the first draft and put forward some suggestions for revision. All authors read and approved the final manuscript.

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Correspondence to Weifeng Ma.

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Ma, W., Li, Y. Periodic Boundary Value Problem for Impulsive Evolution Equations with Noncompact Semigroup. Qual. Theory Dyn. Syst. 22, 110 (2023). https://doi.org/10.1007/s12346-023-00808-w

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  • DOI: https://doi.org/10.1007/s12346-023-00808-w

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