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

Overview & Synopsis

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),c,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.