Existence of pseudo-almost automorphic solutions to some abstract differential equations with Sp-pseudo-almost automorphic coefficients

This paper introduces and studies the notion of Sp-pseudo-almost automorphy (or Stepanov-like pseudo-almost automorphy), which generalizes in a natural fashion the concept of pseudo-almost automorphy that was recently introduced in the literature by Liang, Xiao and Zhang. We next obtain the existence of pseudo-almost automorphic solutions to some differential equations with Sp-pseudo-almost automorphic coefficients.