Asymptotic behavior of solutions of periodic linear partial functional differential equations on the half line

Abstract

We study conditions for the abstract linear functional differential equation x ˙ = A x + F ( t ) x t + f ( t ) , t ≥ 0 to have asymptotic almost periodic solutions, where F ( ⋅ ) is periodic, f is asymptotic almost periodic. The main conditions are stated in terms of the spectrum of the monodromy operator associated with the equation and the circular spectrum of the forcing term f . The obtained results extend recent results on the subject.