Nonautonomous Exponential Dichotomy

On Exponential Dichotomy of Variational Nonautonomous Difference Equations in Banach Spaces

MIHAELA AURELIA TOMESCU University of Petroşani Department of Mathematics and Computer Science University Street 20, 332006 Petroşani ROMANIA [email protected] MIHAIL MEGAN Academy of Romanian Scientists Independenţei 54, 050094 Bucharest ROMANIA West University of Timişoara Department of Mathematics V. Pârvan Blv. No. 4, 300223 Timişoara ROMANIA [email protected] TRAIAN CEAUŞU West University o...

On Exponential Dichotomy of Semigroups

The aim of this paper is to analyze the connections between the exponential dichotomy of a semigroup on a Banach space X and the admissibility of the pair (`p(N, X), `q(N, X)). We obtain necessary and sufficient conditions for exponential dichotomy of exponentially bounded semigroups using discrete time techniques.

Exponential Stability and Exponential Dichotomy of Semigroups of Linear Operators

The aim of this paper is to establish necessary and sufficient conditions for exponential stability of semigroups of linear operators and to show how this conditions can be applied in order to characterize the exponential dichotomy. First, we prove that an exponentially bounded semigroup is exponentially stable if and only if it is (l(N, X), l∞(N, X))-stable, where p ∈ (1,∞). After that this re...

On Exponential Dichotomy of Variational Difference Equations

Discrete Methods and Exponential Dichotomy of Semigroups

The aim of this paper is to characterize the uniform exponential dichotomy of semigroups of linear operators in terms of the solvability of discrete-time equations over N. We give necessary and sufficient conditions for uniform exponential dichotomy of a semigroup on a Banach space X in terms of the admissibility of the pair (l∞(N, X), c00(N, X)). As an application we deduce that a C0-semigroup...