Let Ω be an open subset of ℝn with n≥3 such that 0∈Ω. For s∈(0,2) and q>1 fixed, we consider a positive function u∈C∞(Ω\{0}) such that
| -Δu=u2⋆(s)-1|x|s-uqin Ω\{0}, | (1) |
where 2⋆(s):=2(n-s)n-2 is critical from the viewpoint of the Hardy–Sobolev embeddings. In this talk, I will present recent results on the classification of the behaviour near zero for the positive solutions of (1). This is joint work with Frédéric Robert (University of Lorraine – Nancy).