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Abstract: In this paper we study and obtain the existence of -pseudo almost automorphic solutions to some higher-order differential equations with operator coefficients whose forcing is -pseudo almost automorphic. We next use these abstract results to study the existence of -pseudo almost automorphic solutions to some second-order differential equations in Hilbert space which, among other things, model the so-called linear beam equation. [Copyright &y& Elsevier]

Abstract: In this paper, we make extensive use of the well-known Schauder fixed point principle and the exponential stability of the evolution family involved to study and obtain the existence of almost periodic mild solutions to some classes of nonautonomous higher-order differential equations with operator coefficients in a separable infinite dimensional complex Hilbert space. To illustrate our main result, we study and obtain the existence of an almost periodic mild solution to a wave equation with fractional damping. [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]

Abstract: The paper revisits the concept of -pseudo-almost periodicity recently introduced by the author. In particular, we study the existence of pseudo-almost periodic solutions to some nonautonomous differential equations in the case when the semilinear forcing term is both continuous and -pseudo-almost periodic for . Applications include the existence of pseudo-almost periodic solutions to the heat equation with a forcing term, which is -pseudo-almost periodic and jointly continuous. [Copyright &y& Elsevier]

Abstract: In this paper we give some sufficient conditions, which ensure the existence of pseudo almost periodic solutions to some classes of non-autonomous first-order partial neutral functional-differential with unbounded delay. [Copyright &y& Elsevier]

Abstract: Some sufficient conditions for the existence and uniqueness of pseudo-almost periodic (mild) solutions to some classes of partial evolution equations are given. We then make use of our abstract results to discuss the existence of pseudo-almost periodic solutions to some partial differential equations. [Copyright &y& Elsevier]

Abstract: This paper deals with the existence and uniqueness of pseudo-almost periodic solutions to the semilinear differential equations of the form where are densely defined closed linear operators on a Hilbert space , and is a jointly continuous function. Using both the so-called method of the invariant subspaces for unbounded linear operators and the classical Banach fixed-point principle, the existence of a pseudo-almost periodic solution to (*) is obtained under some suitable assumptions. As applications, we examine the existence and uniqueness of pseudo-almost periodic solutions to some second-order hyperbolic equations. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the pseudo almost periodic solutions to the abstract differential equations of the form:where are densely defined closed linear operators acting in a Hilbert space , and is a -valued pseudo almost periodic function. Using the theory of the invariant subspaces for unbounded linear operators, we show that every bounded solution to is a pseudo almost periodic function. [Copyright &y& Elsevier]

Abstract: In this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti-periodicity, which generalize respectively the well-known notions of periodicity and that of anti-periodicity. Basic properties of these new functions are discussed. Furthermore, the existence of weighted pseudo anti-periodic solutions to some damped non-autonomous second-order differential equations will be investigated. To illustrate our abstract results, the existence of weighted pseudo anti-periodic solutions to a plate-like equation is discussed. [Copyright &y& Elsevier]