Abstract

The authors consider a higher-order abstract functional-differential equation of delay or advanced type. Spectral conditions, such as a new Massera-type criterion, are obtained for the existence of an almost-periodic mild solution of the equation with the same structure of spectrum as that of the forcing term. See also \textit{S.-N. Chow} and \textit{J. K. Hale} [Funkc. Ekvacioj, Ser. Int. 17, 31–38 (1974; Zbl 0297.47048)], \textit{J. L. Massera} [Duke Math. J. 17, 457–475 (1950; Zbl 0038.25002)] and \textit{T. Naito, Nguyen van Minh} and \textit{Jong Son Shin} [Stud. Math. 145, No. 2, 97–111 (2001; Zbl 0982.34074)].