Pseudo-Almost Automorphic Solutions to Some Second-Order Differential Equations

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.

Keywords

• 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