Electron. J. Differential Equations, Vol. 2023 (2023), No. 56, pp. 1-19.

Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems

Yuxin Li, Xiaojun Chang, Zhaosheng Feng

We study the Sobolev critical Schrodinger-Bopp-Podolsky system $$\displaylines{ -\Delta u+\phi u=\lambda u+\mu|u|^{p-2}u+|u|^4u\quad \hbox{in }\mathbb{R}^3,\cr -\Delta\phi+\Delta^2\phi=4\pi u^2\quad \hbox{in } \mathbb{R}^3, }$$ 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 5, 2023.
Math Subject Classifications: 35K92, 35B44, 35B40, 35R02.
Key Words: Normalized solutions; Schrodinger-Bopp-Podolsky system; Lagrange multiplier; ground state; variational method.
DOI: 10.58997/ejde.2023.56

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Yuxin Li
School of Mathematics and Statistics
Northeast Normal University
Changchun, Jilin 130024, China
email: liyx097@nenu.edu.cn
Xiaojun Chang
School of Mathematics and Statistics and
Center for Mathematics and Interdisciplinary Sciences
Northeast Normal University
Changchun, Jilin 130024, China
email: changxj100@nenu.edu.cn
Zhaosheng Feng
School of Mathematical and Statistical Sciences
University of Texas Rio Grande Valley
Edinburg, TX 78539, USA
email: zhaosheng.feng@utrgv.edu

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