Symmetry and Monotonicity of Positive Solutions to Schrödinger Systems with Fractional $p$-Laplacian

Abstract

In this paper, we first establish a narrow region principle and a decay at infinity theorem to extend the direct method of moving planes for general fractional p-Laplacian systems. By virtue of this method, we can investigate the qualitative properties of the following Schrödinger system with fractional p-Laplacian), 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.Mathematics Subject classification (2010): 35R11; 35B06; 35A01.