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

TL;DR

This paper employs the fibering method of Pohozaev to analyze the structure of the Nehari set for a Schrödinger-Poisson system with prescribed mass, revealing both classical and novel results related to specific exponents.

Contribution

It provides a unified approach to old results and introduces new findings on the Nehari set structure for the Schrödinger-Poisson system with prescribed $L^{2}$ norm.

Findings

Clarifies the role of exponents p=3, 8/3, 10/3

Unifies previous results on the Nehari set

Introduces new results in the analysis

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.