A new proof of uniqueness of ground state for pseudo-relativistic Hartree equation

Chen Pan; Zeng xiaoyu

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arXiv · 2608.08493

A new proof of uniqueness of ground state for pseudo-relativistic Hartree equation

Chen Pan·Zeng xiaoyu

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Abstract

We present a new proof of the uniqueness of ground states for the pseudo-relativistic Hartree equation in the non-relativistic regime. The proof treats the Euler-Lagrange equation and the mass constraint as a single augmented system, with the Lagrange multiplier as an additional unknown. The key point is the invertibility of the augmented linearization at the non-relativistic ground state.

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Chen Pan, Zeng xiaoyu. 2026-08-09. A new proof of uniqueness of ground state for pseudo-relativistic Hartree equation. https://arxiv.org/abs/2608.08493

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