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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.

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