C-semigroups and almost periodic solutions of evolution equations ✩

The paper is concerned with the existence of almost periodic mild solutions to evolution equations of the form ˙u(t ) = Au(t )+ f (t), (∗) where A generates a C-semigroup and f is almost periodic. Using the evolution C-semigroup associated with the equation under consideration, we obtain various sufficient conditions for the existence of almost periodic solutions to (∗) which extend previous ones to a more general class of ill-posed equations involving C-semigroups.  2004 Elsevier Inc. All rights reserved