Blow up solutions for one class of system of Pekar–Choquard type nonlinear Schrödinger equation

We prove that firstly the existence of stationary solutions of the Pekar–Choquard system with the formequation(PCS)iϕ→t+Δϕ→+K(ϕ→)+|ϕ→|p-2ϕ→=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.