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

摘要

In this paper, we deal with the existence and multiplicity of positive solutions for the multi-singular semilinear elliptic equations -Δu-∑i=1k μi/|x-ai| 2u=|u|2* -2u+λ| u|q-2u, x∈Ω, where Ω??N(N≥3) is a smooth bounded domain such that the points ai∈Ω, i=1,2,?,k, k≥2, are different, 0≤ μi <μ?=(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.