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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
journal	Annales Henri Poincare
Les DOIs	https://doi.org/10.1007/s00023-026-01736-6
état	Accepté/En presse - 1 janv. 2026

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10.1007/s00023-026-01736-6

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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 - 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.

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

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