Existence and Non-existence of Minimizers for a Multi-particle Model with Concave Nonlinearity

David Gontier; Salma Lahbabi; Simona Rota Nodari

doi:10.1007/s00023-026-01736-6

Existence and Non-existence of Minimizers for a Multi-particle Model with Concave Nonlinearity

David Gontier
, Salma Lahbabi
, Simona Rota Nodari

Université Paris Dauphine
Equipe de Mathématiques Appliquées
Université Hassan II Aïn Chock - Casablanca et LASAARE
Université de Nice
Institut Universitaire de France

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Annales Henri Poincare
DOIs	https://doi.org/10.1007/s00023-026-01736-6
Publication status	Accepted/In press - 1 Jan 2026

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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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AU - Gontier, David

AU - Lahbabi, Salma

AU - Rota Nodari, Simona

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/105047983479

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DO - 10.1007/s00023-026-01736-6

M3 - Article

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SN - 1424-0637

JO - Annales Henri Poincare

JF - Annales Henri Poincare

ER -

Existence and Non-existence of Minimizers for a Multi-particle Model with Concave Nonlinearity

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