On the structure of the Nehari set associated to a Schrödinger-Poisson system with prescribed mass: old and new results

Abstract

In this paper we apply the fibering method of Pohozaev to a Schrödinger-Poisson system, with prescribed $L^2$ norm of the unknown, in the whole ${\mathbb{R}}^3$. The method makes clear the role played by the exponents $p=3,p=8/3,p=10/3$. Beside to show as old results can be obtained in a unified way, we exhibit also new ones.