Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect-Reference-Cited by-同舟云学术

Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect

Published:2022-07-01 Issue:7 Volume:63 Page:071501
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:J. Math. Phys.

Author:

Adami Riccardo¹^ORCID,Boni Filippo²,Carlone Raffaele²,Tentarelli Lorenzo¹^ORCID

Affiliation:

1. Politecnico di Torino, Dipartimento di Scienze Matematiche “G. L. Lagrange,” Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

2. Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni “Renato Caccioppoli,” Via Cintia, Monte S. Angelo, 80126 Napoli, Italy

Abstract

We study the ground states for the Schrödinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every value of the mass; moreover, they are positive, radially symmetric, and decreasing along the radial direction and show a Coulombian singularity at the location of the point interaction. Remarkably, the existence of the ground states is independent of the attractive or repulsive character of the point interaction.

Funder

Ministero dell’Istruzione, dell’Università e della Ricerca

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://aip.scitation.org/doi/pdf/10.1063/5.0091334

Reference31 articles.

1. Singular solitons

2. Singular Mean-Field States: A Brief Review of Recent Results

3. Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs

4. R. Adami, T. Nakamura, and A. Ruighi, “Discontinuous ground states for NLSE on R with a Fülöp-Tsutsuiδinteraction,” arXiv:2010.00895 [math.AP] (2020).

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Two dimensional NLS ground states with attractive Coulomb potential and point interaction;Journal of Differential Equations;2025-01

2. Standing waves and global well-posedness for the 2d Hartree equation with a point interaction;Communications in Partial Differential Equations;2024-03-03

3. Well–posedness of the three–dimensional NLS equation with sphere–concentrated nonlinearity;Nonlinearity;2023-12-05

4. Introduction to the special collection: International congress on mathematical physics 2021;Journal of Mathematical Physics;2023-12-01

5. Failure of scattering for the NLSE with a point interaction in dimension two and three;Nonlinearity;2023-09-01