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arXiv · 2201.00860

Asymptotic profile of ground states for the Schr\"{o}dinger-Poisson-Slater equation

Zeng Liu·Vitaly Moroz
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Abstract

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 $\lambda\to \infty$.

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Zeng Liu, Vitaly Moroz. 2022-01-03. Asymptotic profile of ground states for the Schr\"{o}dinger-Poisson-Slater equation. https://doi.org/10.1016/j.na.2021.112778

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