Normalized ground states for Kirchhoff equations in R3 with a critical nonlinearity

This paper is concerned with the existence of ground states for a class of Kirchhoff type equations in R3 with combined power nonlinearities −a+b∫R3|∇u(x)|2Δu=λu+|u|p−2u+u5 with the restriction ∫R3u2=c2 in the Sobolev critical case 2* = 6 and proves that the problem has a ground state solution (uc,λc)∈S(c)×R for any c > 0, a, b > 0, and 143≤p<6, where S(c)=u∈H1(R3):∫R3u2=c2.