Ground state sign-changing solutions for a Schrodinger-Poisson system with a critical nonlinearity in R-3

In this paper, we investigate the existence of ground state sign-changing solutions to a class of Schrodinger-Poisson systems {-Delta u + u + k(x)phi u = lambda f(x)u + vertical bar u vertical bar(4)u, x is an element of R-3, -Delta phi = k(x)u(2), x is an element of R-3, where k and f are nonnegative functions, 0 < lambda < lambda(1) and lambda(1) is the first eigenvalue of the problem -Delta u + u = lambda f(x)u in H-1 (R-3). With the help of the constraint variational method, we obtain that the Schrodinger-Poisson system possesses at least one ground state sign-changing solution for each 0 < lambda < lambda(l). Moreover, we prove that its energy is strictly larger than twice that of ground state solutions. This paper can be regarded as the complementary work of Huang et al. (2013), Shuai and Wang (2015), Wang and Zhou (2015) and Zhang (2015). (C) 2017 Elsevier Ltd. All rights reserved.