Fractional Hardy-Sobolev elliptic problems - Yang, Jianfu; Yu, Xiaohui (Topological Methods in Nonlinear Analysis, 2020)
In this paper, we study the following singular nonlinear elliptic problem equation cases (-Δ)^ α/ 2 u=λ |u|^r-2u+μ|u|^q-2u|x|^s &in Ω, u=0 &on Ω, cases P equation where Ω is a smooth bounded domain in R^N(N≥ 2) with 0Ω, λ,μ> 0, 0< s≤α, (-Δ)^α/ 2 is the spectral fractional Laplacian operator with 0< α< 2. We establish existence results and nonexistence results of problem eq:1 for subcritical, Sobolev critical and Hardy-Sobolev critical cases.