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Exponential stability concepts for evolution families on \( \mathbb {R}\)

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Abstract

This paper presents some Perron-type results for the nonuniform exponential stability of evolution families on the real line with nonuniform exponential growth. We will mention the notion of the admissibility of the pair \(( \mathcal {L}^p(X), \mathcal {L}^q(X))\), where \( (p,q) \ne (1, \infty )\) and the admissibility of the pair of Schäffer spaces to an evolution family. This notion will be used to obtain new results for the nonuniform exponential stability of an evolution family on \( \mathbb {R}.\)

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Acknowledgments

This work was supported by the strategic grant POSDRU/159/1.5/S/137750, Project “Doctoral and Postdoctoral programs support for increased competitiveness in Exact Sciences research” cofinanced by the European Social Found within the Sectorial Operational Program Human Resources Development 2007–2013.

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Authors and Affiliations

  1. West University of Timişoara, V. Pârvan Blvd. No. 4, Timişoara, 300223, Romania

    Petre Preda, Ciprian Preda & Claudia Morariu

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  1. Petre Preda
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  2. Ciprian Preda
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  3. Claudia Morariu
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Correspondence to Claudia Morariu.

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Communicated by A. Constantin.

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Preda, P., Preda, C. & Morariu, C. Exponential stability concepts for evolution families on \( \mathbb {R}\) . Monatsh Math 178, 611–631 (2015). https://doi.org/10.1007/s00605-014-0726-z

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