Symmetry and monotonicity of positive solutions to Schrodinger systems with fractional p-Laplacians

In this paper, we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems. By virtue of this method, we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian {(-Delta)(p)(s) u + au(p-1) = f(u, v), (-Delta)(p)(t) v + bv(p-1) = g(u, v), where 0 < s, t < 1 and 2 < p < infinity. We obtain the radial symmetry in the unit ball or the whole space R-N (N >= 2), the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g, respectively.