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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]

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 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 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: 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]