Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 56, pp. 1-19.

Title: Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems
       
Authors: Yuxin Li (Northeast Normal Univ., Changchun, Jilin, China)
         Xiaojun Chang (Northeast Normal Univ., Changchun, Jilin, China)
         Zhaosheng Feng (Univ. of Texas Rio Grande Valley, Edinburg, TX, USA)
         
Abstract: 
We study the Sobolev critical Schrodinger-Bopp-Podolsky system
\displaylines{
 -\Delta u+\phi u=\lambda u+\mu|u|^{p-2}u+|u|^4u\quad \text{in }\mathbb{R}^3,\cr
 -\Delta\phi+\Delta^2\phi=4\pi u^2\quad \text{in } \mathbb{R}^3,
}$$
under the mass constraint
$ \int_{\mathbb{R}^3}u^2\,dx=c$
for some prescribed $c>0$, where $2<p<8/3$, $\mu>0$ is a parameter,
and $\lambda\in\mathbb{R}$ is a Lagrange multiplier. By developing a constraint
minimizing approach, we show that the above system admits a local minimizer.
Furthermore, we establish the existence of normalized ground state solutions.

Submitted May 28, 2023. Published September 05, 2023.
Math Subject Classifications: 35K92, 35B44, 35B40, 35R02.
Key Words: Normalized solutions; Schrodinger-Bopp-Podolsky system; Lagrange multiplier; ground state; variational method.