Normalized solutions for Sobolev critical Schrödinger-Bopp-Podolsky systems

Abstract

We study the Sobolev critical Schrödinger-Bopp-Podolsky system \begin{gather*} -Δu+ϕu=λu+μ|u|^{p-2}u+|u|^4u\quad \text{in }\mathbb{R}^3, -Δϕ+Δ^2ϕ=4πu^2\quad \text{in } \mathbb{R}^3, \end{gather*} 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.

19 pages

References in corpus (1)

• Causal approach for the electron-positron scattering in Generalized Quantum Electrodynamics