SS-asymptotically ωω-periodic and asymptotically ωω-periodic solutions to semi-linear Cauchy problems with non-dense domain

In this work, we study the existence and uniqueness of SS-asymptotically ωω-periodic and asymptotically ωω-periodic solutions to a first-order differential equation with linear part dominated by a Hille–Yosida operator with non-dense domain. Applications to partial differential equations, fractional integro-differential and neutral differential equations are given.