Existence of positive ground state solutions for a critical Kirchhoff type problem with sign-changing potential

In this work, we are interested in studying the following Kirchhoff type problem −a+b∫Ω|∇u|2dxΔu=f(x)|u|2∗−2u+λg(x)|u|q−1u,x∈Ω,u=0,x∈∂Ω,where Ω⊂RN(N≥3) is a smooth bounded domain, 2∗=2NN−2 is the critical Sobolev exponent, 00, and f∈L∞(Ω) with the set {x∈Ω:f(x)>0} of positive measures, and g∈L∞(Ω) with g(x)≥0,g≢0. By the Nehari method and variational method, the existence of positive ground state solutions is obtained.