Abstract and Applied Analysis
Volume 2004 (2004), Issue 10, Pages 881-896
doi:10.1155/S1085337504406046
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
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.