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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 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]