Stepanov-like C(n)-pseudo almost automorphy and applications to some nonautonomous higher-order differential equations

Abstract

In this paper we introduce and study a new concept called Stepanov-like $C^{(n)}$-pseudo almost automorphy, which generalizes in a natural fashion both the notions of $C^{(n)}$-pseudo almost periodicity and that of $C^{(n)}$-pseudo almost automorphy recently introduced in the literature by the authors. Basic properties of these new functions are investigated. Furthermore, we study and obtain the existence of $C^{(N+m)}$-pseudo almost automorphic solutions to some nonautonomous higher-order systems of differential equations with Stepanov-like $C^{(m)}$-pseudo almost automorphic coefficients.