We prove that a family of -periodic continuous matrix valued function has an exponential dichotomy with a projector if and only if is bounded uniformly with respect to the parameter and the solution of the Cauchy operator Problem
has a limit in as s tends to which is bounded uniformly with respect to the parameter . Here, is the evolution family generated by , is a real number and q is a fixed positive number.
Submitted February 1, 2013. Published April 5, 2013.
Math Subject Classifications: 47A05, 34D09, 35B35.
Key Words: Periodic evolution families; exponential dichotomy; boundedness.
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| Dhaou Lassoued |
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Université Paris 1 Panthéon-Sorbonne
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email: Dhaou.Lassoued@univ-paris1.fr, firstname.lastname@example.org
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