Fractional nonlinear Schrödinger equations with singular potential in $\mathbf R^n$

We are interested in nonlinear fractional Schrödinger equations with singular potential of form \begin{equation*} (-Δ)^su=\fracλ{|x|^α}u+|u|^{p-1}u,\quad \mathbf R^n\setminus\{0\}, \end{equation*} where $s\in (0,1)$, $α>0$, $p\ge1$ and $λ\in \mathbf R$. Via Caffarelli-Silvestre extension method, we obtain existence, nonexistence, regularity and symmetry properties of solutions to this equation for various $α$, $p$ and $λ$.

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