A Massera type theorem for almost automorphic solutions of differential equations

In this note, we present a Massera type theorem for the existence of almost automorphic solutions of periodic linear evolution equations of the form x (t ) =A(t)x(t)+f (t), where A(t) is unbounded linear operator depending on t periodically and generates a τ -periodic evolutionary process, f is almost automorphic. The main results are stated in terms of the almost automorphy of solutions and their Carleman spectra.  2004 Elsevier Inc. All rights reserved.