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In this paper we study and obtain the existence of a positive almost periodic solution to the nonlinear differential equation with delays that describes the so-called hematopoiesis model. The main tool utilized to establish our existence result consists of the fixed-point theorem in a cone. Two examples are given at the end of the paper to illustrate our main result. [ABSTRACT FROM AUTHOR]

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]

This paper is concerned with the existence of almost periodic mild solutions to some second-order equations. Using dichotomy tools and the Schauder fixed point theorem, the existence of almost periodic mild solutions to those second-order evolution equations is established. To illustrate our abstract results, the existence of almost periodic solutions to a damped second-order boundary value problem is also discussed. [ABSTRACT FROM AUTHOR]

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: In a recent paper by Liang et al. (2010) , the original question which is that of the existence of a weighted mean for almost periodic functions was raised. In particular, they showed through an example that there exist weights for which a weighted mean for almost periodic functions may or may not exist. In this note we give some sufficient conditions which do guarantee the existence of a weighted mean for almost periodic functions, which will then coincide with the classical Bohr mean. Moreover, we will show that under those conditions, the corresponding weighted Bohr transform exists. [Copyright &y& Elsevier]

Abstract: In this paper, under Acquistapace–Terreni conditions, we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations. Applications include the existence of weighted pseudo-almost periodic solutions to a nonautonomous heat equation with gradient coefficients. [Copyright &y& Elsevier]

Abstract: In this paper we introduce the concept of weighted pseudo-almost periodicity in the sense of Stepanov, also called -weighted pseudo-almost periodicity and study its properties. Next, we present a result on the existence of weighted pseudo-almost periodic solutions to the -dimensional heat equation with -weighted pseudo-almost periodic coefficients. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations. Upon making some suitable assumptions, the existence and uniqueness of a weighted pseudo almost periodic solution is obtained. To illustrate our main result, we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional-differential equations with feedback control. [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: The paper considers some new classes of functions called weighted pseudo-almost periodic functions, which implement in a natural fashion the classical pseudo-almost periodic functions due to Zhang. Properties of these weighted pseudo-almost periodic functions are discussed, including a composition result for weighted pseudo-almost periodic functions. The results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo-almost periodic solution to the heat equation with Dirichlet conditions. [Copyright &y& Elsevier]

This paper introduces and examines a new class of functions called Stepanov-like pseudo almost periodic functions (or Sp-pseudo almost periodic functions), which generalizes in a natural fashion the classical notion of pseudo almost periodicity. We then make extensive use of these new functions to study the existence and uniqueness of a pseudo almost periodic solution to the semilinear equation u′(t)=Au(t) + F(t,u(t)), where A : (D)(A) ⊂ X ↦ X is the infinistesimal generator of an exponentially stable C0-semigroup on a Banach space X and F: ℝ × X ↦ X is Sp-pseudo almost periodic for p > 1 and jointly continuous. [ABSTRACT FROM AUTHOR]

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]

The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, some sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those classes of hyperbolic evolution equations are given. As an application, we consider the existence of pseudo almost periodic solutions to the heat equations with delay. [ABSTRACT FROM AUTHOR]

This article deals with the existence and uniqueness of pseudo almost periodic (mild) solutions to the class of partial evolution equations u'(t) = Au(t) +f(t, Bu(t)), t ε R, where A is a sectorial operator on a Banach space X, which is not necessarily densely defined and σ(A) ∩ iR = ... (hyperbolic), B is a linear operator on X, and f : R × Xα ... X is pseudo almost periodic with Xα ⊂ X being an abstract intermediate Banach space. Under some appropriate assumptions, we obtain the existence and uniqueness of such solutions in Xα. An application to semilinear transport-like equations is given. [ABSTRACT FROM AUTHOR]

This paper studies some sufficient conditions for the existence and uniqueness of a pseudo almost periodic mild solution to abstract hyperbolic differential equations with infinite delay. Applications include the existence and uniqueness of a pseudo almost periodic mild solution to the heat equation. [ABSTRACT FROM AUTHOR]