Opuscula Math. 32, no. 3 (2012), 455-471
http://dx.doi.org/10.7494/OpMath.2012.32.3.455
Opuscula Mathematica
Stepanov-like C(n)-pseudo almost automorphy and applications to some nonautonomous higher-order differential equations
Toka Diagana
Valerie Nelson
Gaston M. N'Guérékata
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.
Mathematics Subject Classification: 35B15, 34D09, 58D25, 42A75, 37L05.
- Toka Diagana
- Howard University ,Department of Mathematics, 2441 6th Street, N.W. Washington, D.C. 20059, USA
- Valerie Nelson
- Howard University ,Department of Mathematics, 2441 6th Street, N.W. Washington, D.C. 20059, USA
- Gaston M. N'Guérékata
- Morgan State University, Department of Mathematics, Baltimore, MD 21251, USA
- Received: 2011-08-20.
- Revised: 2011-11-28.
- Accepted: 2011-11-28.
