Massera's theorem for almost periodic solutions of functional differential equations

Dedicated to Professor Yoshiyuki Hino on his sixtieth birthday

抄録

The Massera Theorem for almost periodic solutions of linear periodic ordinary differential equations of the form (*) x^{'}=A(t)x+f(t), where f is almost periodic, is stated and proved. Furthermore, it is extended to abstract functional differential equations (**) x^{'}=Ax+F(t)x_t+f(t), where A is the generator of a compact semigroup, F is periodic and f is almost periodic. The main techniques used in the proofs involve a new variation of constants formula in the phase space and a decomposition theorem for almost periodic solutions.