Symmetry of Positive Solutions to the Coupled Fractional System with Isolated Singularities

In this paper, we consider the following two-coupled fractional Laplacian system with two or more isolated singularities {(-Delta)(s) u = mu(1)u(2q+1) + beta u(p1-1)upsilon(p2), (-Delta)(s) nu + mu(2) nu(2q+1) + beta u(p1) nu(p2-1) in R-n \ Lambda, u > 0, nu > 0, where s is an element of (0, 1) , n > 2s and n >= 2. mu(1), mu(2) and beta are the all positive constants . p(1), p(2) > 1 and p(1) + p(2) -2q + 2 is an element of (2n - 2s/n - 2s, 2n/n - 2s]. Lambda subset of R-n contains finitely many isolated points. By the method of moving plane, we obtain the symmetry results for positive solutions to above system.