Sign-changing solutions for the Schrodinger-Poisson system with concave-convex nonlinearities in R3

In this paper, we consider the following Schr & ouml;dinger-Poisson system { - triangle u + V(x)u + phi u = |u|(p-2)u + lambda K(x)|u|(q-2)u in R-3, - triangle phi = u(2 )in R-3.Under the weakly coercive assumption on V and an appropriate condition on K, we investigate the cases when the nonlinearities are of concave-convex type, that is, 1 < q < 2 and 4 < p < 6. By constructing a nonempty closed subset of the sign-changing Nehari manifold, we establish the existence of least energy sign-changing solutions provided that lambda is an element of (-infinity, lambda(& lowast;)), where lambda(& lowast;) > 0 is a constant.