Sign-changing solutions for the nonlinear Schrodinger-Poisson system in R3

We are interested in the existence and energy estimate of sign-changing solutions for a Schrodinger-Poisson problem on R-3. Because the so-called nonlocal term lambda phi(u)(x) u is involving in the equation, the variational functional of the equation has totally different properties from the case of lambda = 0. By introducing some new ideas, we prove, via a constraint variational method combining the Brouwer degree theory, that the problem has a sign-changing solution under suitable conditions. When lambda = 0, it is known that any sign-changing solution of the problem has an energy exceeding twice the least energy. However, it is still unknown what would happen when lambda > 0. We partially answer this question for lambda > 0 being small.