Geodesic
Uniform exponential stability of linear periodic systems in a Banach space
Electronic journal of differential equations, Tome 2001 (2001)
This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic stability implies the uniform exponential stability. We also show applications to different classes of linear evolution equations, such as ordinary linear differential equations in the space of Banach, retarded and neutral functional differential equations, some classes of evolution partial differential equations.
Classification : 34C35, 34C27, 34K15, 34K20, 58F27
Keywords: non-autonomous linear dynamical systems, global attractors, periodic systems, exponential stability, asymptotically compact systems, equations on Banach spaces 
@article{EJDE_2001__2001__a55,
     author = {Cheban,  D.N.},
     title = {Uniform exponential stability of linear periodic systems in a {Banach} space},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0974.34055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a55/}
}
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%J Electronic journal of differential equations
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Cheban,  D.N. Uniform exponential stability of linear periodic systems in a Banach space. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a55/