Asymptotic behavior of hyperbolic Cauchy problems for Hille-Yosida operators with an application to retarded differential equations

Abstract

In this work, we use the extrapolation methods to study the existence and the uniqueness of bounded and almost periodic, asymptotic almost periodic, pseudo almost periodic and Eberlein-weak almost periodic solutions to hyperbolic Cauchy problems for Hille-Yosida operators d/dtx(t) = Ax(t) + f(t), t ∈ R, when the inhomogeneities f take their values in the extrapolated Favard class corresponding to A.