Positive Ground State Solutions fora Critical Nonlocal Problem in Dimension Three

In this paper,we are interested in the following nonlocal problem with critical exponent{-(a-b∫Ω|▽u|2dx)△u=λ|u|p-2+|u|4u,u=0,x∈Ω,x∂∈Ω,where a,b are positive constants,2<p<6,Ωis a smooth bounded domain in R^(3)andλ>O is a parameter.By variational methods,we prove that problem has a positive ground state solution up forλ>0 sufficiently large.Moreover,we take b as a parameter and study the asymptotic behavior of ub when b↘O.