Exponential ordering for neutral functional differential equations with non-autonomous linear \(D\)-operator (Q650180)

This interesting paper investigates neutral functional differential equations with a stable linear time-dependent \(D\)-operator. Moreover, the operator of convolution \(\widehat{D}\) leaves the space of bounded uniformly continuous mappings in \(C((-\infty,0],{\mathbb R}^n)\) invariant. It is shown that if \(D\) is stable then \(\widehat{D}\) is invertible and, moreover, both \(\widehat{D}\) and \(\widehat{D}^{-1}\) are uniformly continuous in the compact-open topology on bounded sets. A new transformed exponential order is introduced and, under ambient assumptions, the authors derive a \(1\)-covering property for minimal sets. These results are applied to a class of extensively studied compartmental systems yielding information on the amount of material.