Symmetry and monotonicity of positive solutions for a system involving fractional p&q-Laplacian in a ball

In this paper, we study a nonlinear system involving the fractional p&q-Laplacian in the unit ball {(-Delta)(p)(s1) u(x) + (-Delta)(q)(s2)u(x) = u(x)(v(x))(beta), x is an element of B-1(0), (-Delta)(p)(s1)v(x) + (-Delta)(q)(s2)v(x) = v(x)(u(x))(alpha), x is an element of B-1(0), u = v = 0, x is an element of R-n\B-1(0), where 0 < s(1), s(2) < 1, p, q > 2, alpha, beta > 1. By using the direct method of moving planes, we prove that the positive solutions (u, v) of the system must be radially symmetric and monotone decreasing about the origin.