Abstract
For the flow determined by a nonautonomous linear differential equation, we characterize the existence of a strong nonuniform exponential dichotomy in terms of the Fredholm property of a certain linear operator. We consider both cases of one-sided and two-sided exponential dichotomies. Moreover, we use the characterizations to establish the robustness of the notion of a strong nonuniform exponential dichotomy in a simple manner.
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L.B. and C.V. were supported by FCT/Portugal through UID/MAT/04459/2013. D.D. was supported in part by an Australian Research Council Discovery Project DP150100017, Croatian Science Foundation under the Project IP-2014-09-2285 and by the University of Rijeka research Grant 13.14.1.2.02.
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Barreira, L., Dragičević, D. & Valls, C. Nonuniform exponential dichotomies and Fredholm operators for flows. Aequat. Math. 91, 301–316 (2017). https://doi.org/10.1007/s00010-017-0468-9
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DOI: https://doi.org/10.1007/s00010-017-0468-9