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Exponential stability and exponential instability for linear skew-product flows. (English) Zbl 1080.34538

Summary: We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
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