Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems

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. For more inofrmation see https://ejde.math.txstate.edu/Volumes/2023/56/abstr.html