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 Radial symmetry of positive solutions to a class of fractional Laplacian with a singular nonlinearity J. Korean Math. Soc.Published online July 29, 2021 Linfen Cao and Xiaoshan Wang Henan Normal University; Nanjing Normal University Abstract : In this paper, we consider the following nonlocal fractional Laplacian equation with a singular nonlinearity $$(-\Delta)^{s}u(x)=\lambda u^{\beta}(x)+a_{0}u^{-\gamma}(x), ~ x\in \mathbb{R}^{n}$$ where $00$, $1<\beta\leq\frac{n+2s}{n-2s}$, $\lambda>0$ are constants and $a_{0}\geq0$. We use a direct method of moving planes which introduced by Chen-Li-Li to prove the positive solutions $u(x)$ must be radially symmetric and monotone increasing about some point in $\mathbb{R}^{n}$. Keywords : fractional Laplacian, negative powers, method of moving planes, radial symmetry. MSC numbers : 58J35, 35B45. Full-Text :