Browsing by Subject "exponential dichotomy"

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Access status: Open Access ,
Construction of an integral manifold for linear differential-difference equations
(2006) Janglajew, Klara R.; Valeev, Kim G.
In this paper we establish sufficient conditions for the existence of an asymptotic integral manifold of solutions of a linear system of differential-difference equations with a small parameter. This integral manifold is described by a linear system of differential equations without deviating argument.
Access status: Open Access ,
Stepanov-like C(n)-pseudo almost automorphy and applications to some nonautonomous higher-order differential equations
(2012) Diagana, Toka; Nelson, Valerie; N'Guérékata, Gaston Mandata
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.