Blow up solutions for one class of system of Pekar-Choquard type nonlinear Schrodinger equation

We prove that firstly the existence of stationary solutions of the Pekar-Choquard system with the form i (rho) over right arrow (t) + Delta(rho) over right arrow + K((rho) over right arrow) -- vertical bar(rho) over right arrow vertical bar(p-2)(rho) over right arrow = 0, secondly the solutions of Cauchy problem of (PCs) with initial data close to the stationary solution (in a suitable sense) must blow up at finite time; finally the standing wave relating to the stationary solution of (PCs) is strongly unstable in the sense of Definition 4.2. (c) 2006 Elsevier Inc. All rights reserved.