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Admissibility in the Strong and Weak Senses

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Abstract

For a dynamics with continuous time determined by a nonautonomous linear equation, we characterize completely the notion of an exponential dichotomy with respect to a family of norms in terms of an admissibility property. Moreover, we consider both strong and weak admissibility properties, which are expressed, respectively, in terms of classical and mild solutions. As a nontrivial application, we establish the robustness of the notions of an exponential dichotomy with respect to a family of norms and of a nonuniform exponential dichotomy in a very simple manner.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal

    Luis Barreira & Claudia Valls

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  1. Luis Barreira
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  2. Claudia Valls
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Correspondence to Luis Barreira.

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Partially supported by FCT/Portugal through UID/MAT/04459/2013.

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Barreira, L., Valls, C. Admissibility in the Strong and Weak Senses. Qual. Theory Dyn. Syst. 19, 20 (2020). https://doi.org/10.1007/s12346-020-00359-4

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  • DOI: https://doi.org/10.1007/s12346-020-00359-4

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