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Zbl 1221.34141
Barreira, Lu{\'\i}s; Valls, Claudia
(English)
[J] Discrete Contin. Dyn. Syst. 30, No. 1, 39-53 (2011). ISSN 1078-0947; ISSN 1553-5231/e

The authors investigate the relation between the notions of exponential stability and admissibility, in the general context of nonuniform exponential behavior. It is shown that, with respect to certain adapted norms related to the nonuniform behavior, if any $L^p$ ($1<p\leq \infty$) space is admissible for a given evolution process, then this process is a nonuniform exponential dichotomy. For each nonuniform exponential dichotomy, the paper provides a collection of admissible Banach spaces.
[Jialin Hong (Beijing)]
MSC 2000:
*34D09 Dichotomy, trichotomy
34D08 Lyapunov exponents
34C45 Method of integral manifolds
34D10 Stability perturbations of ODE

Keywords: admissibility; nonuniform exponential dichotomy; differential systems

Cited in: Zbl pre06011212

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