Least energy sign-changing solutions for a class of Schrodinger-Poisson system on bounded domains

This paper is concerned with the Schrodinger-Poisson system -Delta u + phi u = lambda u + mu|u|(2)u and -Delta phi = u(2) setting on a bounded domain Omega subset of R-3 with smooth boundary and lambda,mu is an element of R being parameters. By using variational techniques in combination with the nodal Nehari manifold method, we show the existence of (mu) over bar > 0 such that for all (lambda,mu)is an element of(-infinity,lambda(1))x((mu) over bar,+infinity), the above system has one least energy sign-changing solution, where lambda(1) > 0 is the first eigenvalue of (-Delta,H-0(1)(Omega)). The results of this paper are complementary to those in Alves and Souto [Z. Angew. Math. Phys. 65, 1153-1166 (2014)].