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Barycentric Solutions of Linear Almost Periodic Equations: Baire Class and Almost Automorphy

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Abstract

When the Favard separation condition fails, a linear almost periodic equation possessing bounded solutions may have no almost periodic solutions, or equivalently, no continuous solutions in hull. Almost automorphic solutions are however known to persist and, in the scalar case, the same happens to semi-continuous solutions in the hull. The aim of the present paper is twofold: extending the second type of solutions to higher dimensions, via the notion of barycenter, and fully understanding the relationships with the first type of solutions. Semi-continuity has to be replaced by some Baire class and the scalar connection with almost automorphy breaks down in an unrecoverable way: a not negligible effort is devoted to restore it at deeper level of generality.

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Authors and Affiliations

  1. Universidad de Granada, 18071, Granada, Spain

    Juan Campos

  2. Università di Milano, Via Saldini 50, 20133, Milan, Italy

    Massimo Tarallo

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  1. Juan Campos
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  2. Massimo Tarallo
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Correspondence to Juan Campos.

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Campos, J., Tarallo, M. Barycentric Solutions of Linear Almost Periodic Equations: Baire Class and Almost Automorphy. J Dyn Diff Equat 32, 1475–1509 (2020). https://doi.org/10.1007/s10884-019-09792-9

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  • DOI: https://doi.org/10.1007/s10884-019-09792-9

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