Almost Automorphic Solution for Semilinear Non-autonomous Differential Equations in Banach Spaces

An investigation was made into the almost automorphic solution for the semi-linear non-autonomous differential equations in Banach spaces. By theory of evolution family, the existence and uniqueness of the almost automorphic solution for the semi-linear non-autonomous differential equation ddtu(t) = A(t)u(t)+h(t) is proved. Then by Banach fixed point theo- rem, the existence and uniqueness of the almost automorphic solution for the semi-linear non-autonomous differential equation dtu(t) = A(t)u(t) +f(t,u(t)) is also proved.