Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems
DOI:
https://doi.org/10.58997/ejde.2023.56Keywords:
Normalized solutions; Schrodinger-Bopp-Podolsky system; Lagrange multiplier; ground state; variational methodAbstract
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.
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