Yuxin Li, Xiaojun Chang, Zhaosheng Feng
Abstract:
We study the Sobolev critical Schrodinger-Bopp-Podolsky system
$$\displaylines{
-\Delta u+\phi u=\lambda u+\mu|u|^{p-2}u+|u|^4u\quad \hbox{in }\mathbb{R}^3,\cr
-\Delta\phi+\Delta^2\phi=4\pi u^2\quad \hbox{in } \mathbb{R}^3,
}$$
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
Show me the PDF file (410 KB), TEX file for this article.
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Yuxin Li School of Mathematics and Statistics Northeast Normal University Changchun, Jilin 130024, China email: liyx097@nenu.edu.cn |
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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 |
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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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