Symmetry of Positive Solutions to Quasilinear Fractional Systems

Using the method of moving planes, we establish the radial symmetry of positive solutions to the fractional system {(-Delta)(p)(s)u = f(u, v), (-Delta)(q)(t)v = g(u, v) in the entire Euclidean space R-n and in the unit ball, where 0 < s, t < 1 and p, q >= 2. In particular, our result can be applied to the nonlinearities f (u, v) u(a)v(b) and g(u, v) u(c)v(d), where a, d is an element of R and b, c > 0.