Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations

The paper revisits the concept of SpSp-pseudo-almost periodicity recently introduced by the author. In particular, we study the existence of pseudo-almost periodic solutions to some nonautonomous differential equations in the case when the semilinear forcing term is both continuous and SpSp-pseudo-almost periodic for p>1p>1. Applications include the existence of pseudo-almost periodic solutions to the heat equation with a forcing term, which is SpSp-pseudo-almost periodic and jointly continuous.