On ground state solutions for a Kirchhoff type equation with critical growth

Abstract

In this paper, with the aid of variational method and concentration-compactness principle, a positive ground state solution is obtained for a class of Kirchhoff type equations with critical growth {−(a+b∫R3|∇u|2dx)Δu=u5+λk(x)uq−1,x∈R3,u∈D1,2(R3), where λ>0 is a parameter, 2<q<6 and k satisfies some conditions.