Symmetry of Singular Solutions for a Weighted Choquard Equation Involving The Fractional p-Laplacian

Let  be a positive solution, which may blow up at zero, of the equation

where 0 < s < 1, 0 < β < n, p > 2, q ≥ 1 and α > 0. We prove that if u satisfies some suitable asymptotic properties, then u must be radially symmetric and monotone decreasing about the origin. In stead of using equivalent fractional systems, we exploit a direct method of moving planes for the weighted Choquard nonlinearity. This method allows us to cover the full range 0 < β < n
in our results.