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

摘要

We prove that firstly the existence of stationary solutions of the Pekar–Choquard system with the form(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.