Dhaou Lassoued
Abstract:
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 Laboratoire SAMM EA4543 Université Paris 1 Panthéon-Sorbonne centre P.M.F., 90 rue de Tolbiac 75634 Paris cedex 13, France email: Dhaou.Lassoued@univ-paris1.fr, dhaou06@gmail.com |
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