Symmetry of Positive Solutions to Choquard Type Equations Involving the Fractional p-Laplacian

We study symmetric properties of positive solutions to the Choquard type equation

where 0 < s < 1, 0 < α < n, p ≥ 2, q > 1, r > 0, a ≥ 0 and  is the fractional p-Laplacian. Via a direct method of moving planes, we prove that every positive solution u which has an appropriate decay property must be radially symmetric and monotone decreasing about some point, which is the origin if a > 0.