Almost periodicity for some nonautonomous evolution equations with nondense domain: application to some epidemic models

The main objective of this study is to investigate the existence and uniqueness of almost periodic solutions for some nondense nonautonomous linear evolution equations with Stepanov forcing term. This investigation is carried out in cases where the semigroup associated with the linear part of equation is not necessarily compact. We prove new results of Bohr–Neugebauer and Massera type. Next, we investigate the uniqueness of an almost periodic solution when the semigroup associated with the linear part has an exponential dichotomy. Serval examples are provided for illustration.