Asymptotic properties of non-relativistic limit for pseudo-relativistic Hartree equations
Abstract
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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Advanced Mathematical Physics Problems
Geometry and complex manifolds
Publication details
- Journal / source
- Journal of Functional Analysis
- Volume
- 292
- Issue
- 2
- Pages
- 111664–111664
- Publication date
- 24 August 2026
- Language
- EN