Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev exponent

In this work, we are interested in considering the following nonlocal problem −a+b∫Ω|∇u|2dxΔu=μ|u|2∗−2u+λ|u|q−2u,x∈Ω,u=0,x∈∂Ω,where Ω⊂RN(N≥4) is a smooth bounded domain, a≥0,b>0,10 and 2∗=2NN−2 is the critical Sobolev exponent. By using the variational method and the critical point theorem, some existence and multiplicity results are obtained.