Polynomial stability of evolution operators in Banach spaces
The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
On (h; k)-Dichotomy and (h; k)-Trichotomy of Noninvertible Evolution Operators in Banach Spaces
Abstract The paper considers some concepts of (h, k)-dichotomy and (h, k)-trichotomy for noninvertible evolution operators in Ba- nach spaces. A characterization of the (h, k)-trichotomy of an evolution operator in terms of (h, k)-dichotomy for two associated evolution operators is given. As applications of this result, charac- terizations for nonuniform exponential trichotomy and nonuniform polynomial trichotomy are obtained.
Dichotomies and Asymptotic Formulas for the Solutions of Differential Equations
Abstract The new concept of (h, k)-dichotomy is studied extensively and is used in asymptotic equivalence problems.