Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 89, pp. 17.
Exponential dichotomy of nonautonomous periodic systems in terms of
the boundedness of certain periodic Cauchy problems
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 PanthéonSorbonne
centre P.M.F., 90 rue de Tolbiac
75634 Paris cedex 13, France
email: Dhaou.Lassoued@univparis1.fr, dhaou06@gmail.com

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