Geodesic
Uniform exponential stability of linear almost periodic systems in Banach spaces
Electronic journal of differential equations, Tome 2000 (2000)
This article is devoted to the study linear non-autonomous dynamical systems possessing the property of uniform exponential stability. We prove that if the Cauchy operator of these systems possesses a certain compactness property, then the uniform asymptotic stability implies the uniform exponential stability. For recurrent (almost periodic) systems this result is precised. We also show application for different classes of linear evolution equations: ordinary linear differential equations in a Banach space, retarded and neutral functional differential equations, and some classes of evolution partial differential equations.
Classification : 34C35, 34C27, 34K15, 34K20, 58F27, 34G10
Keywords: non-autonomous linear dynamical systems, global attractors, almost periodic system, exponential stability, asymptotically compact systems 
@article{EJDE_2000__2000__a108,
     author = {Cheban,  D.N.},
     title = {Uniform exponential stability of linear almost periodic systems in {Banach} spaces},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0944.37046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a108/}
}
TY  - JOUR
AU  - Cheban,  D.N.
TI  - Uniform exponential stability of linear almost periodic systems in Banach spaces
JO  - Electronic journal of differential equations
PY  - 2000
VL  - 2000
UR  - http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a108/
LA  - en
ID  - EJDE_2000__2000__a108
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%0 Journal Article
%A Cheban,  D.N.
%T Uniform exponential stability of linear almost periodic systems in Banach spaces
%J Electronic journal of differential equations
%D 2000
%V 2000
%U http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a108/
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%F EJDE_2000__2000__a108
Cheban,  D.N. Uniform exponential stability of linear almost periodic systems in Banach spaces. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a108/