带势的非线性Schrdinger方程的爆破性质

The Blow-up Property of Nonlinear Schrdinger Equations with Potential

讨论了带势的非线性Schrd inger方程iφt=-Δφ+V(x)φ-|φ|p-1φ,其中t≥0,x∈RN.运用能量方法,得到了一个较为简单的判别条件,当初值满足该条件时,Cauchy问题的解在有限时间爆破.

A class of nonlinear Schrōdinger equations with potential of the form iφl=-△φ＋V（x）φ-｜φ｜^p-1φ,is discussed, where t ≥0 ,x ∈R^N. By using energy method, a relatively simple criterion is obtained. When the condition in the criterion is satisfied, the solution of the equation above will blow up in finite time.