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In this paper we introduce and study a new concept called C(n)-pseudo-almost automorphy, which generalizes in a natural fashion both the notions of C(n)-almost periodicity and that of C(n)-almost automorphy. Properties of such a new concept will be studied. Furthermore, we prove the existence of C(n)-pseudo-almost automorphic solutions to some n-order differential equations. [ABSTRACT FROM AUTHOR]

In this article, first we introduce and study the concept of Sγp-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in Sγp-pseudo almost automorphic spaces. To illustrate our abstract result, we will study the existence and uniqueness of a pseudo almost automorphic solution to the heat equation with a negative time-dependent diffusion coefficient. [ABSTRACT FROM AUTHOR]

Abstract: The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results. [Copyright &y& Elsevier]

Abstract: This paper introduces and studies the notion of -pseudo-almost automorphy (or Stepanov-like pseudo-almost automorphy), which generalizes in a natural fashion the concept of pseudo-almost automorphy that was recently introduced in the literature by Liang, Xiao and Zhang. We next obtain the existence of pseudo-almost automorphic solutions to some differential equations with -pseudo-almost automorphic coefficients. [Copyright &y& Elsevier]

In this paper we obtain the existence of almost automorphic solutions for some neutral first-order functional differential equations with Spalmost automorphic coefficients. [ABSTRACT FROM AUTHOR]

This article is concerned with the existence and uniqueness of an almost automorphic solution to the semilinear equation [image omitted] where [image omitted] is the infinitesimal generator of an exponentially stable C0-semigroup on a Banach space [image omitted] and [image omitted] is Sp-almost automorphic for p > 1 and jointly continuous. [ABSTRACT FROM AUTHOR]