On Asymptotic Periodic Solutions of Delay Evolution Equations on the Half Line

Abstract

We establish necessary and sufficient conditions for the existence of asymptotic periodic solutions of delay evolution equations on half line. These conditions are determined by the spectrum of forcing term and spectrum of evolution semigroups associated with the equations. Our goal is to extend on Massera's theorem by recalling a new concept of solutions, namely, asymptotic solutions for evolution equations in Banach spaces, which have potential applications to partial differential equations as well as abstract functional differential equations.