Normalized solutions for Schrödinger-Bopp-Podolsky system

Abstract: In this paper, we study the following energy functional originates from the Schr\"{o}dinger-Bopp-Podolsky system $$I(u)=\frac{1}{2}\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx+\frac{1}{4}\int_{\mathbb{R}^{3}} \phi_{u}u^{2}dx-\frac{1}{p}\int_{\mathbb{R}^{3}}|u|^{p}dx$$ constrained on $B_{\rho}=\left{u\in H^{1}(\mathbb{R}^{3},C):\ \left|u\right|{2}=\rho\right},$ where $\rho>0.$ As such constrained problem $I(u)$ is bounded from below on $B{\rho}$ when $p\in(2,\frac{10}{3}).$ We use minimizing method to get a normalized solution.