Almost Periodic Solutions of C-well-posed Evolution Equations

This paper is concerned with the existence and uniqueness of almost periodic mild solutions of evolution equations of the form u(t) = Au(t) + ƒ(t) where A is the generator of a holomorphic Csemigroup on a Banach space and ƒ is an almost periodic function. A sufficient condition in terms of spectral properties of A and ƒ is obtained that extends a well known result in this subject.