Opuscula Mathematica
Opuscula Math. 32, no. 3 (), 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




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.
Cite this article as:
Toka Diagana, Valerie Nelson, Gaston M. N'Guérékata, Stepanov-like C(n)-pseudo almost automorphy and applications to some nonautonomous higher-order differential equations, Opuscula Math. 32, no. 3 (2012), 455-471, http://dx.doi.org/10.7494/OpMath.2012.32.3.455
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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