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Almost periodicity and almost automorphy for some evolution equations using Favard’s theory in uniformly convex Banach spaces

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Abstract

In this work, we use an approach due to Favard (Acta Math 51:31–81, 1928) to study the existence of weakly almost periodic and almost automorphic solutions for some evolution equation whose linear part generates a \(C_{0}\)-group satisfying the Favard condition in uniformly convex Banach spaces. When this \(C_{0}\)-group is bounded, which is a condition stronger than Favard’s condition, we prove the equivalence between almost automorphy and weak almost automorphy of solutions.

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Acknowledgments

The authors would like to thank the referees for their valuable suggestions and comments.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakesh, Morocco

    Brahim Es-sebbar & Khalil Ezzinbi

Authors
  1. Brahim Es-sebbar
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  2. Khalil Ezzinbi
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Correspondence to Brahim Es-sebbar.

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Communicated by Abdelaziz Rhandi.

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Es-sebbar, B., Ezzinbi, K. Almost periodicity and almost automorphy for some evolution equations using Favard’s theory in uniformly convex Banach spaces. Semigroup Forum 94, 229–259 (2017). https://doi.org/10.1007/s00233-016-9810-0

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  • DOI: https://doi.org/10.1007/s00233-016-9810-0

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