关于三个方程的半线性椭圆方程组的Pohozaev等式

A POHOZAEV IDENTITY FOR SEMILINEAR ELLIPTIC SYSTEM WITH THREE EQUATIONS

考虑半线性椭圆方程组△u+f(v)=0,x∈Ω,△v+g(w)=0,x∈Ω,△w+h(u)=0,x∈Ω,u=v=w=0,x∈Ω,的Pohozaev等式,其中ΩRn是有界区域,u,v,w∈C2(Ω)∩C1(-Ω),f、g、h:R→R是连续函数.

In this article, we consider the Pohozaev identity about a class of semilinear elliptic systems {△u＋f（v）=0,x∈Ω △v＋g（w）=0,x∈Ω △w＋h（u）=0,x∈Ω u=v=w=0,x∈δΩ where Ω∪→R^n Rn is a bounded domain, u,v,w∈C^2（Ω）∩↓C^1（Ω）,and f、g、h：R→R are continuous functions.