Symmetry of solutions for a fractional p-Laplacian equation of Choquard type

Let  and be a positive solution of the equation

We prove that if u satisfies some decay assumption at infinity, then u must be radially symmetric and monotone decreasing about some point in . Instead of using equivalent fractional systems, we exploit a generalized direct method of moving planes for fractional p-Laplacian equations with nonlocal nonlinearities. This new approach enables us to cover the full range 0<α<n in our results.