Concentration behavior of ground state solutions for a fractional Schrodinger-Poisson system involving critical exponent

We are concerned with the existence and concentration behavior of ground state solutions of the fractional Schrodinger-Poisson system with critical nonlinearity {epsilon(2s) (-Delta)(s)u + V (x)u + phi u - lambda vertical bar u vertical bar(p-2)u+vertical bar u vertical bar 2*(s) -2u in R-3, epsilon(2t) (-Delta)t phi = u(2) in R-3, where epsilon > 0 is a small parameter, lambda > 0, 4s +2t/s+t < p < 2(s)* = 6/3-ss, (-Delta)(alpha) denotes the fractional Laplacian of order alpha = 8, t is an element of (0, 1) and satisfies 2t + 2s > 3. The potential V is continuous and positive, and has a local minimum. We obtain a positive ground state solution for epsilon > 0 small, and we show that these ground state solutions concentrate around a local minimum of V as epsilon -> 0.