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Zbl 1034.34056
Megan, Mihail; Sasu, Bogdan; Sasu, Adina Luminiţa
On nonuniform exponential dichotomy of evolution operators in Banach spaces. (English)
[J] Integral Equations Oper. Theory 44, No. 1, 71-78 (2002). ISSN 0378-620X; ISSN 1420-8989/e

The authors study the nonuniform exponential dichotomy of evolution operators in Banach spaces. It is shown that $(C_0,C_0)$-admissibility for evolution operators implies nonuniformly exponentially dichotomy, and that the converse generally does not as an example shows. This paper is related to the paper of {\it Nguyen Van Minh, F. Räbiger} and {\it R. Schnaubelt} [Integral Equations Oper. Theory 32, 332--353 (1998; Zbl 0977.34056)], which discussed the uniform case.
[Yuan Rong (Beijing)]

MSC 2000:: *34D09 Dichotomy, trichotomy
34D05 Asymptotic stability of ODE

Keywords: nonuniform exponential dichotomy; $(C_0, C_0)$-admissibility; evolution operator.

Citations: Zbl 0977.34056

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