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On nonuniform exponential dichotomy of evolution operators in Banach spaces. (English) Zbl 1034.34056

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 Nguyen Van Minh, F. Räbiger and R. Schnaubelt [Integral Equations Oper. Theory 32, 332–353 (1998; Zbl 0977.34056)], which discussed the uniform case.

MSC:

34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations

Citations:

Zbl 0977.34056
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References:

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