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arXiv · 2512.01655

Normalized solutions for the planar Schrödinger-Poisson system with two electrons interaction

Baihong Li·Yuanhong Wei·Xiangjian Zeng
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Abstract

This paper focuses on the normalized solutions for the planar Schrödinger-Poisson system with a two-electron interaction, which models the effect between electrons and the electrostatic potential they generate. As the parameters vary, some existence results are established. Specifically, a ground state solution is obtained for some general cases. The existence of two solutions is established for the mass-supercritical case, one of which is a ground state solution and the other one is an excited state solution. We develop a compactness method to deal with the functionals involving logarithmic convolution terms. The Pohožaev identity for the coupled Schrödinger-Poisson system with a logarithmic convolution term is also shown, which is crucial for addressing the mass-supercritical problem.

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Baihong Li, Yuanhong Wei, Xiangjian Zeng. 2025-12-01. Normalized solutions for the planar Schrödinger-Poisson system with two electrons interaction. https://arxiv.org/abs/2512.01655

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