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

Diagana T., Nelson V., N'Guerekata G. M.

Opuscula Mathematica

2012

Vol. 32, no. 3

455-471

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.

A new composition theorem for sp-weighted pseudo almost periodic functions and applications to semilinear differential equations

Zhao Z., Chang Y., N'Guerekata G. M.

Opuscula Mathematica

2011

Vol. 31, no. 3

457-474

In this paper, we establish a new composition theorem for Sp-weighted pseudo almost periodic functions under weaker conditions than the Lipschitz ones currently encountered in the literatures. We apply this new composition theorem along with the Schauder's fixed point theorem to obtain new existence theorems for weighted pseudo almost periodic mild solutions to a semilinear differential equation in a Banach space.