摘要 : In this paper, we apply the direct method of moving planes to a type of fractional Laplacian equation both in the whole space and the half space. Instead of conventional extension method and the equivalent integral method, we work... 展开 In this paper, we apply the direct method of moving planes to a type of fractional Laplacian equation both in the whole space and the half space. Instead of conventional extension method and the equivalent integral method, we work directly on the fractional Laplacian equation. Using this method, we are able to obtain symmetry and non-existence of positive solutions. This method can also be employed to Schrodinger equations and Lane-Emden equations. 收起