一类带调和势的非线性Klein-Gordon方程

The Instability of a Class of Nonlinear Coupled System

运用能量和微分、积分不等式技巧,讨论一类带调和势的非线性Klein-Gordon方程utt-Δu+|x|2u+mu=a|u|pu+b|u|qu,x∈RN,t>0,其中,u=u(t,x):R+×RN→C的初值问题,得到了在一定条件下解的不稳定性质。

A class nonlinear Klein-Gordon equation with harmonic potential：utt-△u＋｜x｜^2u＋mu=a｜u｜^pu＋b｜u｜^qu,x∈R^N,t〉0,其中,u=u（t,x）：R^＋×R^N→Cis studied. The instability of the solution of the system isobtained.