Asymptotic properties of non-relativistic limit for pseudo-relativistic Hartree equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912971530174464 |
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| author | Chen, Pan Zelati, Vittorio Coti Wei, Yuanhong |
| author_facet | Chen, Pan Zelati, Vittorio Coti Wei, Yuanhong |
| contents | In this paper, we study the asymptotic behavior of energy and action ground states to the following pseudo-relativistic Hartree equation \[ \left(\sqrt{-c^2Δ+m^2c^4}-mc^2\right)u + λu = \left(|x|^{-1}*|u|^2\right)u \] as the speed of light $c\to\infty$.
We obtain an asymptotic expansion of the ground state as $c \to \infty,$ which is new in the case of the energy ground state and generalizes the results of Choi, Hong, and Seok (2018) for the action ground state. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_05917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic properties of non-relativistic limit for pseudo-relativistic Hartree equations Chen, Pan Zelati, Vittorio Coti Wei, Yuanhong Analysis of PDEs 35Q40 35J50 49J35 In this paper, we study the asymptotic behavior of energy and action ground states to the following pseudo-relativistic Hartree equation \[ \left(\sqrt{-c^2Δ+m^2c^4}-mc^2\right)u + λu = \left(|x|^{-1}*|u|^2\right)u \] as the speed of light $c\to\infty$. We obtain an asymptotic expansion of the ground state as $c \to \infty,$ which is new in the case of the energy ground state and generalizes the results of Choi, Hong, and Seok (2018) for the action ground state. |
| title | Asymptotic properties of non-relativistic limit for pseudo-relativistic Hartree equations |
| topic | Analysis of PDEs 35Q40 35J50 49J35 |
| url | https://arxiv.org/abs/2505.05917 |