Unbounded Perturbations of C0-Semigroups on Banach Spaces and Applications

In this paper we prove a perturbation result for strongly continuous semigroups extending one of G. Weiss from Hilbert to Banach spaces. This allows us to establish a new variation of constants formula for non-homogeneous perturbed Cauchy problems. From this formula we deduce another new one for non-homogeneous functional differential equations with L^p-phase spaces in terms of Yosida extensions of delay operators.