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

Abstract

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 Schrödinger system with fractional p-Laplacian

$$\left\{ {\matrix{{( - \Delta )_p^su + a{u^{p - 1}} = f(u,v),} \cr {( - \Delta )_p^tv + b{v^{p - 1}} = g(u,v),} \cr } } \right.$$

where 0 < s, t < 1 and 2 < p < ∞. 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.