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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.


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

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

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Electronic Journal of Differential Equations



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Mathematics Commons



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