Moving planes for nonlinear fractional Laplacian equation with negative powers
Moving planes for nonlinear fractional Laplacian equation with negative powers
In this paper, we study symmetry properties of positive solutions to the fractional Laplace equation with negative powers on the whole space. We can use the direct method of moving planes introduced by Jarohs-Weth-Chen-Li-Li to prove one particular result below. If $u∈ C^{1, 1}_{loc}(\mathbb{R}^{n})\cap L_{α}$ satisfies \begin{document}$(-Δ)^{α/2}u(x)+u^{-β}(x) = 0, \ …