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In this paper we study the well-posedness for some damped elastic systems in a Banach space. To illustrate our abstract results, we study the existence of classical solutions to some elastic systems with viscous and strong dampings. [ABSTRACT FROM AUTHOR]

This paper is aimed at studying the existence of square-mean almost periodic solutions to some singular stochastic differential equations with square-mean almost periodic coefficients. Using the block diagonal form of a linear operator on the suitable space, we establish an existence result under some appropriate assumptions. [ABSTRACT FROM AUTHOR]

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]

Abstract: In this paper we study and obtain the existence of an almost automorphic solution to a Beverton–Holt dynamic equation with a nonconstant survival rate under some reasonable assumptions. [Copyright &y& Elsevier]

Abstract: In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations with pseudo-almost automorphic coefficients. In order to illustrate our main results, we will study the existence of pseudo-almost automorphic solutions to a structurally damped plate-like boundary value problem. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a new theory for asymptotically almost automorphic sequences on which is a natural generalization of the concept of asymptotically almost periodicity for sequences due to Ky Fan. We next make extensive use of such a newly introduced concept as well as discrete dichotomy techniques to study and establish the existence of globally attracting almost automorphic solutions to some higher-order nonautonomous difference equations. [Copyright &y& Elsevier]

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: 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: In this paper we obtain the existence of solutions to some classes of partial fractional differential equations. Applications include the existence of solutions to a fractional heat-like equation. [Copyright &y& Elsevier]

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]

Abstract: This paper studies suitable sufficient conditions to ensure the existence and uniqueness of weighted pseudo-almost periodic solutions to a neutral delay integral equation of advanced type introduced by T.A. Burton in the literature. The abstract results are then utilized to characterize weighted pseudo-almost periodic solutions to the well-known logistic equation. [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 the existence and uniqueness of almost automorphic mild solutions to some classes of first-order partial neutral functional-differential equations. Sufficient conditions for the existence and uniqueness of almost automorphic mild solutions to the above-mentioned equations are obtained. As an application, a first-order boundary value problem arising in control systems is considered. [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]

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: We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations. [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: We study the existence and uniqueness of pseudo-almost-periodic solutions to semilinear differential equations of the form where is the infinitesimal generator of an analytic semigroup acting on a (complex) Banach space , and is a jointly continuous function. Under some additional assumptions on and , the existence and uniqueness of a pseudo-almost-periodic (classical) solution to (∗) is obtained by using both fractional powers of operators and the Banach’s fixed-point principle. [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]