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Zbl 1242.34114
Preda, Ciprian; Preda, Petre; Praţa, Cristina
An extension of some theorems of L. Barreira and C. Valls for the nonuniform exponential dichotomous evolution operators. (English)
[J] J. Math. Anal. Appl. 388, No. 2, 1090-1106 (2012). ISSN 0022-247X

This paper extends some recent results by {\it L. Barreira} and {\it 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.
[Minh Van Nguyen (Carrollton)]

MSC 2000:: *34G20 Nonlinear ODE in abstract spaces
34D09 Dichotomy, trichotomy

Keywords: nonuniformly exponential boundedness; strongly continuous evolution family; admissibility; nonuniformly exponential dichotomy

Citations: Zbl 1228.34090

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