The authors consider evolution equations of the form
in a complex Banach space . A continuous function is almost automorphic if for any sequence of real numbers, there exists a subsequence such that
for all . The uniform spectrum of a bounded, continuous function , denoted by , is defined and its properties are investigated. Let be a closed subset of and let is almost automorphic and . Assuming that is an infinitesimal generator of an analytic semigroup of linear operators on and , the existence and uniqueness of a mild solution in of (1) are proven if and only if , where denotes the spectrum of . Letting , it follows that there exists a unique almost automorphic mild solution of (1) such that .