Favard – Amerio theory for almost periodic functional-differential equations without the use of $H$-classes of these equations

Abstract

The Favard – Amerio theory is constructed for almost periodic functional-differential equations in a Banach space without the use of $\scr H$ -classes of these equations. For linear equations, we present the first example of an almost periodic operator, which has no analogs in the classical Favard – Amerio theory.