Exponential dichotomy for evolution families on the real line

Adina Luminiţa Sasu

Abstract and Applied Analysis, 2006, vol. 2006, 1-16

Abstract:

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair ( L p ( ℝ , X ) , L q ( ℝ , X ) ) . We show that the admissibility of the pair ( L p ( ℝ , X ) , L q ( ℝ , X ) ) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p ≥ q . As applications we obtain characterizations for uniform exponential dichotomy of semigroups.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:031641

DOI: 10.1155/AAA/2006/31641

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