Abstract
In a paper from 2010, Barreira and Valls (J Differ Equ 249:2889–2904, 2010) use Lyapunov norms to set up admissibility conditions for nonuniform exponential contractions. In 2011, the same authors extend their analysis from Barreira and Valls (J Differ Equ 249:2889–2904, 2010) to the case of nonuniform exponential dichotomy for linear evolution families with (non)uniform exponential growth (see Barreira and Valls in Discret Contin Dyn Syst 30(1):39–53, 2011). Following their approach, we are able to choose appropriate “test-functions” to establish admissibility-type conditions for the existence of a (non)uniform exponential dichotomy of a strongly continuous cocycle with (non)uniform exponential growth.
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Bătăran, F., Preda, C. & Preda, P. Extending Some Results of L. Barreira and C. Valls to the Case of Linear Skew-Product Semiflows. Results Math 72, 965–978 (2017). https://doi.org/10.1007/s00025-017-0666-8
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DOI: https://doi.org/10.1007/s00025-017-0666-8