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An extension of some theorems of L. Barreira and C. Valls for the nonuniform exponential dichotomous evolution operators. (English) Zbl 1242.34114
This paper extends some recent results by L. Barreira and C. Valls in [J. Differ. Equations 249, No. 11, 2889–2904 (2010; Zbl 1228.34090)] on nonuniform exponential stability to nonuniform exponential dichotomy. The main result gives a sufficient condition for the nonuniform exponential dichotomy for a strongly continuous evolution family in terms of the admissibility of two function spaces.
MSC:
34G20Nonlinear ODE in abstract spaces
34D09Dichotomy, trichotomy
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