Exponential trichotomy of differential systems

Integral Equations and Exponential Trichotomy of Skew-Product Flows

We are interested in an open problem concerning the integral characterizations of the uniform exponential trichotomy of skew-product flows. We introduce a new admissibility concept which relies on a double solvability of an associated integral equation and prove that this provides several interesting asymptotic properties. The main results will establish the connections between this new admissi...

Lyapunov Function and Exponential Trichotomy on Time Scales

Trichotomy for Dynamical Systems in Banach Spaces

We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept of ω-trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coeffi...

Solutions of Exponential Growth to Systems of Partial Differential Equations

This result is very deep and its proof rather long and intricate. In the present paper we show that if one restricts attention to C ~ functions on R n which are of exponential growth, it is possible to derive the formula by classical methods. Moreover, it is possible to obtain the measures featuring in the representation explicitly in terms of the represented solution. A's a fringe benefit we a...

Impulsive Exponential Stabilization of Functional Differential Systems with Infinite Delay