A Massera-type criterion for almost periodic solutions of higher-order delay or advance abstract functional differential equations

Abstract

Let $u$ be a given bounded uniformly continuous mild solution of a higher-order abstract functional differential equation of delay or advance type. We give a so-called Massera-type criterion for the existence of a mild solution, which is a “spectral component” of $u$ with spectrum similar to the one of the forcing term $f$. Various spectral criteria for the existence of almost periodic and quasiperiodic mild solutions are given.