Variation of constants formula and almost periodic solutions for some partial functional differential equations with infinite delay

In this work, we give a variation of constants formula for partial functional differential equations with infinite delay. We assume that the linear part is not necessarily densely defined and its resolvent operator satisfies the Hille–Yosida condition. We establish a reduction of the problem to a finitedimensional space which allows us to prove the existence of almost periodic solutions. © 2005 Elsevier Inc. All rights reserved.