Uniform exponential stability of linear almost periodic systems in Banach spaces

• Main Author: David N. Cheban
• Format: Article
• Language: English
• Published: Texas State University 2000-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: non-autonomous linear dynamical systems; global attractors; almost periodic system; exponential stability; asymptotically compact systems.
• Online Access: http://ejde.math.txstate.edu/Volumes/2000/29/abstr.html

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.