Nonuniform exponential dichotomies and admissibility

Pages: 39 - 53, Volume 30, Issue 1, May 2011

doi:10.3934/dcds.2011.30.39       Abstract        References        Full Text (378.5K)       Related Articles

Luís Barreira - Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (email)
Claudia Valls - Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (email)

Abstract: In this paper we consider the relation between the notions of exponential stability and admissibility, in the general context of nonuniform exponential behavior. In particular, we show that with respect to certain adapted norms related to the nonuniform behavior, if any $L^p$ space, with $p\in(1,\infty]$, is admissible for a given evolution process, then this process is a nonuniform exponential dichotomy. In addition, for each nonuniform exponential dichotomy we provide a collection of admissible Banach spaces, also defined in terms of the adapted norms.

Keywords:  Admissibility, nonuniform exponential dichotomy.
Mathematics Subject Classification:  Primary: 34D09, 37D25.

Received: January 2010;      Revised: May 2010;      Published: February 2011.

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