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On the Perron-Bellman theorem for evolutionary processes with exponential growth in Banach spaces. (English) Zbl 0972.47027
The necessary and sufficient conditions for exponential stability of an evolutionary process on a Banach space with an exponential growth are given. They generalize the known results obtained for strongly continuous one parameter semigroups.

MSC:
47D06 One-parameter semigroups and linear evolution equations
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