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Pseudo-Almost Automorphic Solutions to Some Second-Order Differential EquationsKeywords: exponential stability , sectorial operator , hyperbolic semigroup , almost automorphic , pseudo-almost automorphic , autonomous second-order differential equation , Sine-Gordon equation , amenability , Banach modules , module amenability , weak module amenability , semigroup algebra , inverse semigroup Abstract: In this paper we study and obtain the existence of pseudo-almost automorphic solutions to some classes of second-order abstract differential equations on a Hilbert space. To illustrate our abstract results, we discuss the existence of pseudo almost automorphic solutions to the N-dimensional Sine-Gordon boundary value problem. En este trabajo se estudia y obtiene la existencia de soluciones casi-seudo automorfas a algunas clases de ecuaciones diferenciales abstractas de segundo orden en un espacio de Hilbert. Para ilustrar nuestros resultados abstractos, se discute la existencia de soluciones casi-seudo automorfas en el problema de contorno N-dimensional de Sine-Gordon.
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