Bounded solutions of an abstract differential equation of special form with delayed argument
The differential equation with delayed argument \[ x^\prime(t) = A_1 x(t) + A_2 x(t-1)+y(t),\quad t\in \mathbb{R} \] is considered, where the unknown function \(x\) maps \(\mathbb{R}\) into a complex Banach space. There are two results which establish necessary conditions for the existence and uniqueness of a bounded solution with bounded derivative.
scientific article; zbMATH DE number 6157080