Electron. J. Diff. Eqns., Vol. 2001(2001), No. 03, pp. 1-12.

Uniform exponential stability of linear periodic systems in a Banach space

D. N. Cheban

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.

Submitted August 28, 2000. Published January 3, 2001.
Math Subject Classifications: 34C35, 34C27, 34K15, 34K20, 58F27, 4G10.
Key Words: non-autonomous linear dynamical systems, global attractors, periodic systems, exponential stability, asymptotically compact systems, equations on Banach spaces.

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David N. Cheban
State University of Moldova
Faculty of Mathematics and Informatics
60, A. Mateevich str.
Chisinau, MD-2009, Moldova
e-mail: cheban@usm.md

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