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

In this paper, we deal with the existence and multiplicity of positive solutions for the multi-singular semilinear elliptic equations −Δu−∑i=1kμi|x−ai|2u=|u|2∗−2u+λ|u|q−2u,x∈Ω, where Ω⊂RN(N≥3) is a smooth bounded domain such that the points ai∈Ωai∈Ω, i=1,2,…,ki=1,2,…,k, k≥2k≥2, are different, 0≤μi<μ̄=(N−22)2, λ>0λ>0, 1≤q<21≤q<2, and 2∗=2NN−2. The results depend crucially on the parameters λλ, qq and μiμi for i=1,2,…,ki=1,2,…,k.