Remarks about a fractional Choquard equation: Ground state, regularity and polynomial decay

With appropriate hypotheses on the nonlinearity f, we prove the existence of a ground state solution u for the problem {(- Delta(p))(s)u + A vertical bar u vertical bar(p-2) u = (1/vertical bar x vertical bar(mu) * F(u)) f(u) in R-N, where 0 < mu < N, (-Delta(p))(s) stands for the (s, p)-Laplacian operator, F is the primitive of f and A is a positive constant. When mu < p, we also show that u is an element of L-infinity (R-N) boolean AND C-0 (R-N) and has polynomial decay. (C) 2017 Elsevier Ltd. All rights reserved.