Asymptotic behaviour for the 3-D Schrodinger-Poisson system in the attractive case with positive energy

In this paper, we study the asymptotic behaviour of solutions to the three- dimensional Schrodinger-Poisson system in the attractive case with positive energy. In this case, it is proved that for a real initial condition, the solutions expand unboundedly as time goes to infinity. The proof of this re sult is based on the derivation of a dispersive equation relating density a nd linear momentum, as well as on optimal bounds for the kinetic energy. (C ) 1999 Elsevier Science Ltd. All rights reserved.