Kirchhoff方程单峰解的局部唯一性

Local Uniqueness of a Single Peak Solution of a Subcritical Kirchhoff Problem in R^3

该文主要证明了以下非线Kirchhoff问题的单峰解的局部唯一性-(∈^2a+∈b∫R^3|▽u|^2dx)△u+u=K(x)|u|^(p-1)u,u> 0,x∈R^3,其中∈>0任意小,a,b> 0,1<p<5,K:R^3→R是连续有界函数.该文主要采用反证法结合局部的Pohozeav恒等式进行证明.

In this paper,we obtain the local uniqueness of a single peak solution to the following Kirchhoff problem-(∈^2 a+∈b∫R^3|▽u|^2dx)△u+u=K(x)|u|^(p-1)u,u>0,x∈R^3,for∈>0 sufficiently small,where a,b>0 and 1<p<5 are constants,K:R^3→R is a bounded continuous function.We mainly use a contradiction argument developed by Li G,Luo P,Peng S in[20],applying some local pohozaev identities.Our result is totally new for Kirchhoff equations.