On the ground state solution for a critical fractional Laplacian equation

In this paper, we study the existence of ground state solutions for the following critical fractional Laplacian equation {(−Δ)α2u=|u|2α∗−2u+μuinΩ,u=0on∂Ω, where 0<α<2,Ω⊂RN,N>(1+2)α is a bounded domain. We will prove that the problem possesses a nontrivial ground state solution for any μ>0μ>0.