Abstract

This paper is concerned with the existence of almost periodic solutions of neutral functional differential equations of the form \(\frac{d} {dt}Dx_t=Lx_t+f(t)\), where \(D,L\) are bounded linear operators from the function space \({\mathcal C}:=C([-r,0],\mathbb{C}^n\), \(f\) is an almost periodic function. We prove a Massera criterion for almost periodic solutions saying that if this equation has a bounded solution, then it has an almost periodic solution with the same structure of spectrum as the one of \(f\).