A new proof of uniqueness of ground state for pseudo-relativistic Hartree equation
Chen Pan, Zeng xiaoyu
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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