Abstract and Applied Analysis
Volume 2004 (2004), Issue 10, Pages 881-896

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

Nguyen Van Minh1 and Ha Binh Minh2

1Department of Mathematics, State University of West Georgia, Carrollton 30118, GA, USA
2Department of Applied Mathematics, Hanoi University of Technology, Khoa Toan, Dai Hoc Bach Khoa Hanoi, 1 Dai Co Viet Road, Hanoi, Vietnam

Received 24 January 2003

Copyright © 2004 Nguyen Van Minh and Ha Binh Minh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.