Asymptotic profile of least energy solutions to the nonlinear Schrodinger-Bopp-Podolsky system

We consider the nonlinear Schr"odinger-Bopp-Podolsky system in \(\mathbb{R}^3\): $$\displaylines{ - \Delta v + v + \phi v = v |v|^{p - 2}, \cr \beta^2 \Delta^2 \phi - \Delta \phi = 4 \pi v^2, }$$ where \(\beta > 0\) and \(3 < p < 6\); the unknowns being \(v\) and \(\phi \colon \mathbb{R}^3 \to \mathbb{R}\). We prove that, as \(\beta \to 0\) and up to translations and subsequences, the least energy solutions of the above converge to a least energy solution to the nonlinear Schrodinger-Poisson system in \(\mathbb{R}^3\): $$\displaylines{ - \Delta v + v + \phi v = v |v|^{p - 2}, \cr - \Delta \phi = 4 \pi v^2. }$$ For more information see https://ejde.math.txstate.edu/Volumes/2025/29/abstr.html

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Publication Details

Journal
Electronic Journal of Differential Equations
Published
2025-03-17
DOI
https://doi.org/10.58997/ejde.2025.29
Primary Topic
Advanced Mathematical Physics Problems
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article
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article

Asymptotic profile of least energy solutions to the nonlinear Schrodinger-Bopp-Podolsky system

Gustavo de Paula Ramos
Electronic Journal of Differential Equations
Advanced Mathematical Physics Problems
article

Asymptotic profile of least energy solutions to the nonlinear Schrodinger-Bopp-Podolsky system

Gustavo de Paula Ramos
article en

Abstract

We consider the nonlinear Schr\"odinger-Bopp-Podolsky system in \(\mathbb{R}^3\): $$\displaylines{ - \Delta v + v + \phi v = v |v|^{p - 2}, \cr \beta^2 \Delta^2 \phi - \Delta \phi = 4 \pi v^2, }$$ where \(\beta > 0\) and \(3 < p < 6\); the unknowns being \(v\) and \(\phi \colon \mathbb{R}^3 \to \mathbb{R}\). We prove that, as \(\beta \to 0\) and up to translations and subsequences, the least energy solutions of the above converge to a least energy solution to the nonlinear Schrodinger-Poisson system in \(\mathbb{R}^3\): $$\displaylines{ - \Delta v + v + \phi v = v |v|^{p - 2}, \cr - \Delta \phi = 4 \pi v^2. }$$ For more information see https://ejde.math.txstate.edu/Volumes/2025/29/abstr.html

Electronic Journal of Differential EquationsVol. 2025(01-??)
Universidade de São Paulo (BR)
Openalex Percentile: Top 91%
Advanced Mathematical Physics Problems
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