Asymptotically almost periodic mild solutions for some partial integrodifferential inclusions using scale of Banach spaces

We are interested in the existence of mild solutions for a class of partial integrodifferential inclusions in infinite dimensional Banach spaces. First, we show the existence of mild solutions with the help of a scale of Banach spaces, the theory of resolvent operators, and the fixed point theory fo...

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Bibliographic Details
Published in:Nonautonomous Dynamical Systems 2023-11, Vol.10 (1), p.91-112
Main Authors: El Matloub, Jaouad, Ezzinbi, Khalil
Format: Article
Language:English
Subjects:
45K05
47D06
47H10
asymptotically almost periodic solution
integrodifferential inclusions
measures of noncompactness and condensing mappings
mild solution
resolvent operator
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Summary:We are interested in the existence of mild solutions for a class of partial integrodifferential inclusions in infinite dimensional Banach spaces. First, we show the existence of mild solutions with the help of a scale of Banach spaces, the theory of resolvent operators, and the fixed point theory for the measure of non-compactness. Moreover, we examine the existence of asymptotically almost periodic solutions for our problem. Finally, an example of the abstract results is provided.
ISSN:2353-0626
2353-0626
DOI:10.1515/msds-2023-0102