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

• Main Authors: Toka Diagana, Ahmed Mohamed
• Format: Article
• Language: English
• Published: Universidad de La Frontera 2011-10-01
• Series: Cubo
• Subjects: 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
• Online Access: http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300007
• ISSN: 0716-7776; 0719-0646

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.<br>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.