Uniqueness of Ground State Solutions for a Defocusing Hartree Equation via Inverse Optimal Problems
Analysis of PDEs
2026-01-22 v1
Abstract
We study a generalized defocusing Hartree equation with nonlocal exchange potential and repulsive Hartree--Fock interaction. Using an inverse optimal problem (IOP) approach, we prove the existence and uniqueness of ground state solutions. Additionally, we establish the existence of principal solutions, their continuous dependence on parameters, and a dual variational formulation. The IOP method provides a systematic framework for addressing inverse problems in nonlocal Schr\"{o}dinger operators and offers new insights into the structure of solutions for defocusing Hartree-type equations.
Keywords
Cite
@article{arxiv.2601.14591,
title = {Uniqueness of Ground State Solutions for a Defocusing Hartree Equation via Inverse Optimal Problems},
author = {Yavdat Il'yasov and Juntao Sun and Nur Valeev and Shuai Yao},
journal= {arXiv preprint arXiv:2601.14591},
year = {2026}
}