GROUND STATE SOLUTIONS FOR THE PERIODIC FRACTIONAL SCHRODINGER-POISSON SYSTEMS WITH CRITICAL SOBOLEV EXPONENT

We study the fractional Schrodinger-Poisson system with critical Sobolev exponent {(-Delta)(s)u + V(x)u + phi u = f (x, u) + K (x)vertical bar u vertical bar(2s)*(-2)u in R-3, (-Delta)(t)phi = u(2) in R-3, where (-Delta)(alpha) denotes the fractional Laplacian of order alpha = s, t is an element of (0, 1); V(x), f (x, u) and K(x) are 1-periodic in the x-variables; 2(s)* = 6/(3 - 2s) is the fractional critical Sobolev exponent in dimension 3. Under some weaker conditions on f, we prove the existence of ground state solutions for such a system via the mountain pass theorem in combination with the concentration-compactness principle. Our results are new even for s = t = 1.