Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 29, pp. 1-18.
Title: Uniform exponential stability of linear almost periodic systems
in Banach spaces
Author: D. N. Cheban (State Univ. of Moldova, Chisinau, Moldova)
Abstract:
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.
Submitted January 4, 2000. Published April 17, 2000.
Math Subject Classifications: 34C35, 34C27, 34K15, 34K20, 58F27, 34G10.
Key Words: non-autonomous linear dynamical systems; global attractors;
almost periodic system; exponential stability; asymptotically compact systems.