A sign-changing solution for the Schrödinger-Poisson equation in $\mathbb R^3$
Claudianor O. Alves, Marco A. S. Souto, Sérgio H. Monari Soares · Rocky Mountain Journal of Mathematics · 2017
We find a sign-changing solution for a class of Schr\"odinger-Poisson systems 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.