Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator

Abstract

We study neutral functional differential equations with stable linear non-autonomous D-operator. The operator of convolution D* transforms BU into BU. We show that, if D is stable, then D* is invertible and, besides, D* and its inverse are uniformly continuous for the compact-open topology on bounded sets. We introduce a new transformed exponential order and, under convenient assumptions, we deduce the 1-covering property of minimal sets. These conclusions are applied to describe the amount of material in a class of compartmental systems extensively studied in the literature.