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.

Keywords

• pseudo almost automorphic \(C^{(n)}\)-pseudo almost automorphy
• Stepanov-like \(C^{(n)}\)-pseudo almost automorphy
• exponential dichotomy