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

Abstract

In this paper we apply the fibering method of Pohozaev to a Schr\"odinger-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.