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

Abstract

Let [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] be a positive solution of the equation [Formula: see text] We prove that if [Formula: see text] satisfies some decay assumption at infinity, then [Formula: see text] must be radially symmetric and monotone decreasing about some point in [Formula: see text]. Instead of using equivalent fractional systems, we exploit a generalized direct method of moving planes for fractional [Formula: see text]-Laplacian equations with nonlocal nonlinearities. This new approach enables us to cover the full range [Formula: see text] in our results.