Existence and concentration of ground state solutions for doubly critical Schrodinger-Poisson-type systems

In this paper, we are concerned with the existence and concentration of ground state solutions for the following nonlinear Schrodinger-Poisson-type system with doubly critical growth {-epsilon(2)Delta u + V (x)u - phi vertical bar u vertical bar(3)u = vertical bar u vertical bar(4)u + f(u), in R-3, -epsilon(2)Delta phi = vertical bar u vertical bar(5), in R-3, where epsilon > 0 is a small parameter. By employing the concentration-compactness principle and mountain pass theorem, we prove the existence of positive ground state solutions v(epsilon) with exponential decay at infinity for epsilon sufficiently small under some suitable assumptions on the potential V and nonlinearity f. Moreover, as epsilon -> 0(+), v(epsilon) concentrates around a global minimum point of V.