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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 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 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: 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: 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]