Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 03, pp. 1-12.
Title: Uniform exponential stability of linear periodic systems in a Banach space
Author: D. N. Cheban (State Univ. of Moldova, Moldova)
Abstract:
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.