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

In this paper, we study a nonlinear system involving the fractional p&q-Laplacian in R-n { (-Delta)(p)(s1) u(x) + (-Delta(s2)(q) u(x) = f (u(x), v(x)), x is an element of R-n, (-Delta)(p)(s1) u(x) + (-Delta(s2)(q) u(x) = g (u(x), v(x)), x is an element of R-n, u, v > 0, x is an element of R-n. where 0 < s(1), s(2) < 1, p, q > 2. By using the direct method of moving planes, we prove that the positive solution (u, v) of system above must be radially symmetric and monotone decreasing in the whole space.