Existence and concentration of positive ground state solutions for nonlinear fractional Schrodinger-Poisson system with critical growth

A In this paper, we study the following fractional Schrodinger-Poisson system involving competing potential functions { epsilon(2s)(-Delta)(s)u + V(x)u + phi u = K(x)f(u) + Q(x)vertical bar u vertical bar(2*s-2)u, in R-3, epsilon(2t)(-Delta)(t) phi = u(2), in R-3, where epsilon > 0 is a small parameter, f is a function of C-1 class, superlinear and subcritical nonlinearity, 2*(s) = 6/3-2s, s > 3/4, t is an element of (0, 1), V(x), K(x), and Q(x) are positive continuous functions. Under some suitable assumptions on V, K, andQ, we prove that there is a family of positive ground state solutionswith polynomial growth for sufficiently small epsilon > 0, of which it is concentrating on the set of minimal points of V(x) and the sets of maximal points of K(x) and Q(x).