Multiple positive solutions for a semilinear equation with critical exponent and prescribed singularity

This paper is devoted to the study of a semilinear equation of the form: −Δu−μV(x)u=|u|2∗−2u+θh(x),u∈H01(Ω), where Ω⊂RN(N≥3)Ω⊂RN(N≥3) is an open bounded domain with smooth boundary ∂Ω∂Ω, 0<μ<μ̄=(N−22)2, 2∗=2NN−2, h(x)>0h(x)>0 and V(x)V(x) has prescribed finitely many singular points. Using variational methods, we establish some existence and multiplicity of positive solutions for the problem.