Normalized solutions for Sobolev critical Schrödinger-Bopp-Podolsky systems

Authors

Yuxin Li
Xiaojun Chang
Zhaosheng Feng, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

9-5-2023

Abstract

We study the Sobolev critical Schr¨odinger-Bopp-Podolsky system −∆u + φu = λu + µ|u|p−2u + |u|4u in R3, −∆φ + ∆2φ = 4πu2 in R3, under the mass constraint u2 dx = c R3 for some prescribed c > 0, where 2 < p < 8/3, µ > 0 is a parameter, and λ ∈ 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.

Comments

© 2023. This work is licensed under a CC BY 4.0 license.

Recommended Citation

Li, Yuxin, Xiaojun Chang, and Zhaosheng Feng. 2023. “Normalized Solutions for Sobolev Critical Schrodinger-Bopp-Podolsky Systems.” Electronic Journal of Differential Equations 2023 (56): 1–19. https://doi.org/10.58997/ejde.2023.56

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Electronic Journal of Differential Equations

DOI

10.58997/ejde.2023.56