Existence and asymptotic behaviour for the solutions of the coupled Klein-Gordon-Schrodinger equations

This paper is concerned with the existence, uniqueness and uniform decay for the solutions of the coupled Klein-Gordor-Schrodinger damped equations ipsi(t) + Delta(psi), + i \psi\(2) psi + igammapsi = -phipsi in Omega X (0, infinity) phi(tt) - Deltaphi + mu(2)phi + F (phi, phi(t)) = beta\psi\(2theta) in Omega x (0, infinity) where Q is a bounded domain of R-n, n less than or equal to 3, F : R-2 --> R is a C-1-function; gamma, 0, 0 are constants such that gamma, beta > 0 and I less than or equal to 2theta less than or equal to 2.