Fractional nonlinear Schrödinger equations with singular potential in Rn

We are interested in nonlinear fractional Schrödinger equations with singular potential of form (−Δ)su=λ|x|αu+|u|p−1u,x∈Rn{0}, where s ∈ (0, 1), α > 0, p ≥ 1, and λ ∈ R. Via the Caffarelli-Silvestre extension method, we obtain existence, nonexistence, regularity, and symmetry properties of solutions to this equation for various α, p, and λ.