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

  • Toka Diagana Department of Mathematics, Howard University, 2441 6th Street N.W., Washington, D.C. 20059 - USA.
  • Ahmed Mohamed Department of Mathematics, Howard University, 2441 6th Street N.W., Washington, D.C. 20059 - USA.
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

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.

Published
2011-10-01
How to Cite
[1]
T. Diagana and A. Mohamed, “Pseudo-Almost Automorphic Solutions to Some Second-Order Differential Equations”, CUBO, A Mathematical Journal, vol. 13, no. 3, pp. 117–139, Oct. 2011.