Normalized solutions for Schrödinger–Bopp–Podolsky system with a negative potential

Abstract

In this paper, we study a class of Schrödinger–Bopp–Podolsky systems with a negative potential $V\left(x\right)$ in $R^3$. By using Mountain-Pass argument and detailed analysis of the energy level value, we obtain a normalized solution with positive energy under suitable assumptions on $V\left(x\right)$. Moreover, we also prove that there is no normalized solutions with negative energy.