Asymptotic profile of ground states for the Schr\'{o}dinger-Poisson-Slater equation
| Autor: | Liu, Zeng, Moroz, Vitaly |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.na.2021.112778 |
| Popis: | We study the Schr\"{o}dinger-Poisson-Slater equation $$-\Delta u + u+\lambda(I_{2}*|u|^2)u=|u|^{p-2}u\quad\text{in $\mathbb R^3$},$$ where $p\in (3,6)$ and $\lambda>0$. By using direct variational analysis based on the comparison of the ground state energy levels, we obtain a characterization of the limit profile of the positive ground states for $\lambda\to \infty$. Comment: 7 pages |
| Databáze: | arXiv |
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