Ground State Sign-Changing Solutions for Critical Schrodinger-Poisson System with Steep Potential Well

We investigate a class of nonlinear Schrodinger-Poisson system : ? - ?u + V lambda(x)u + phi u= |u|4u+ |u|p-2u in Pi 83, - ?phi = u2 in Pi 83, where p is an element of (5, 6) and V lambda(x) = lambda V(x) + 1 with lambda > 0. Under some mild assumptions on V, the existence of ground state sign-changing solution is obtained for lambda > 0 large enough by adopting constrained minimization arguments and analytical techniques. At the same time, we also study the asymptotic behavior of sign-changing solutions as lambda -> infinity.