A sign-changing solution for the Schr\"odinger-Poisson equation
  We find a sign-changing solution for a class of Schr\"odinger-Poisson system in $\mathbb{R}^3$ as an existence result by minimization in a closed subset containing all the sign-changing solutions of the equation. The proof is based on variational methods in association with the deformation lemma and Miranda's theorem. 
Claudianor O. Alves, Marco A. S. Souto, S\'ergio H. M. Soares
math.AP