Dependence results on almost periodic and almost automorphic solutions of evolution equations

We consider the semilinear evolution equations $x'(t) = A(t) x(t) + f(x(t), u(t),t)$ and $x'(t) = A(t) x(t) + f(x(t), zeta,t)$ where $A(t)$ is a unbounded linear operator on a Banach space X and f is a nonlinear operator. We study the dependence of solutions x with respect to the function $u$ in three cases: the continuous almost periodic functions, the differentiable almost periodic functions, and the almost automorphic functions. We give results on the continuous dependence and on the differentiable dependence.