Abstract and Applied Analysis

Abstract and Applied Analysis / 2006 / Article

Open Access

Volume 2006 |Article ID 031641 | https://doi.org/10.1155/AAA/2006/31641

Adina Luminiţa Sasu, "Exponential dichotomy for evolution families on the real line", Abstract and Applied Analysis, vol. 2006, Article ID 031641, 16 pages, 2006. https://doi.org/10.1155/AAA/2006/31641

Exponential dichotomy for evolution families on the real line

Received20 Oct 2004
Accepted26 Sep 2005
Published26 Apr 2006

Abstract

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

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Copyright © 2006 Adina Luminiţa Sasu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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