Existence of Almost periodic solutions for functional differential equation

如果我们考虑一个发展方程，它是无穷时滞偏微分方程组的推广，相空间有两种类型，一种是一致衰减记忆空间，一种是衰落记忆空间。在本文中，我们讨论了上述方程：(I)相空间和分解.(Ii)Liapunov方法和概周期解的存在定理.(Iii)线性系统的存在定理.(Iv)非线性系统的概周期解的存在性.特别是用常数公式证明了概周期解和概自同构解的存在性定理.这些都是周期系统的Massera型定理的推广。并且，解的玻尔谱继承了微扰项的玻尔谱。

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.