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arXiv · 2509.04952

Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity

David Gontier·Salma Lahbabi·Simona Rota Nodari
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Abstract

We study a multi--particle model including a kinetic energy and a non linear local self-interaction, both in the bosonic and fermionic cases. In both cases, we prove that the model is well-posed if the number of particles is large enough. In particular, we show that there is a nonlinearity for which the model with $N=2$ particles is well-posed, while the model with $N=1$ is not.

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David Gontier, Salma Lahbabi, Simona Rota Nodari. 2025-09-05. Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity. https://arxiv.org/abs/2509.04952

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