Multiple positive solutions for semilinear elliptic equations involving multi-singular inverse square potentials and concaveconvex nonlinearities

In this paper, we deal with the existence and multiplicity of positive solutions for the multi-singular semilinear elliptic equations -Δu-∑_i=1^k μi/|x-a_i| ²u=|u|^{2* -2}u+λ| u|^q-2u, x∈Ω, where Ω⊂ℝ^N(N≥3) is a smooth bounded domain such that the points a_i∈Ω, i=1,2,⋯,k, k≥2, are different, 0≤ μi <μ̄=(N-2/2)², λ>0, 1≤q<2, and 2* =2N/N-2. The results depend crucially on the parameters λ, q and ^μi for i=1,2,⋯,k.