Hyperbolicity via Admissibility in Delay Equations

摘要

We show that the notion of an exponential dichotomy for a nonautonomous linear delay equation can be characterized in terms of an admissibility property. After introducing Banach spaces where we take the perturbations of the linear equation and where we look for the solutions, we show that the existence of an exponential dichotomy is equivalent to the admissibility of this pair of spaces. We consider the general cases of delay equations satisfying the Caratheodory conditions and of noninvertible evolution families defined by the linear equations. Moreover, we consider delay equations on the line and on the half-line.