Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with Sp-weighted pseudo-almost periodic coefficients

In this paper we introduce the concept of weighted pseudo-almost periodicity in the sense of Stepanov, also called Sp-weighted pseudo-almost periodicity and study its properties. Next, we present a result on the existence of weighted pseudo-almost periodic solutions to the NN-dimensional heat equation with Sp-weighted pseudo-almost periodic coefficients.