Conditional Stability of Semigroups and Periodic Solutions to Evolution Equations

Abstract

We prove the existence and uniqueness of periodic solutions to linear and semilinear evolution equations. Our method is based on the analysis of the conditional stability of the semigroups generated by the corresponding linear equations and connection with the choice of the initial data from which emanates the periodic solution. We also give applications to damped wave equations and damped Timoshenko beam systems.