R^3中一类带临界指数的Kirchhoff型问题的注记

Remark on a Class of Kirchhoff-Type Problem with Critical Exponent in R^3

研究如下一类带临界指数的Kirchhoff型问题:{-a+b∫R^3|u|^2dxΔu=u^5+λk(x)uq-1 x∈R^3u∈D^1,2(R^3)其中a,b,λ>0,2<q<6,k∈L6/6-q(R^3)为非零非负函数.利用变分方法,获得了一个正山路解.进一步,证明了正基态解的存在性.补充并完善了近期相关文献的结果.

In this paper, the following Kirchhoff-type problem with critical exponent is considered:- a+b∫ R^3 | u|^ d x Δ u=u^5 +λk(x)u^ q-1 x∈ R 3 u∈D^1,2 ( R^3 ) where a,b,λ>0, 2<q<6, k∈L 6/-q ( R^3 ) is nonzero and nonnegative. By using the variational method, a positive Moutian-Pass solution is obtained and the existence of positive ground state solution is proved, which complete and improve some results of the recent reference.