Existence of Almost periodic solutions for functional differential equation

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If we consider an evolution equations which is a generalization of partial differential equations with infinite delay, The phase space has two types, that is, one is a uniform fading memory space and the other is a fading memory space. In this report, we have the followings for the above equations :(i)Phase space and decompositions.(ii)Liapunov's method and existence theorems of almost periodic solutions.(iii)existence theorem for linear systems.(iv)existence of almost periodic solution for nonlinear systems.In particular, existence theorems of almost periodic solutions and almost automorphic solutions are shown by using the constant formula. These are generalizations of Massera Type theorems for periodic systems. And, Bohr spectrum of the solutions are inherited from that of perturbed terms.