@article{4022b77ba14547dda4f9fe13110d5ede,
title = "On stability and instability of standing waves for 2d-nonlinear Schr{\"o}dinger equations with point interaction",
abstract = "We study existence and stability properties of ground-state standing waves for two-dimensional nonlinear Schr{\"o}dinger equation with a point interaction and a focusing power nonlinearity. The Schr{\"o}dinger operator with a point interaction (−Δα)α∈R describes a one-parameter family of self-adjoint realizations of the Laplacian with delta-like perturbation. The operator −Δα always has a unique simple negative eigenvalue eα. We prove that if the frequency of the standing wave is close to −eα, it is stable. Moreover, if the frequency is sufficiently large, we have the stability in the L2-subcritical or critical case, while the instability in the L2-supercritical case.",
keywords = "Instability, Nonlinear Schr{\"o}dinger equation, Point interaction, Stability, Standing wave",
author = "Noriyoshi Fukaya and Vladimir Georgiev and Masahiro Ikeda",
note = "Funding Information: NF was supported by JSPS KAKENHI Grant Number JP20K14349 . VG was partially supported by Project {\textquoteleft}Problemi stazionari e di evoluzione nelle equazioni di campo non-lineari dispersive” of GNAMPA – Gruppo Nazionale per l'Analisi Matematica 2020, by the project PRIN 2020XB3EFL by the Italian Ministry of Universities and Research , by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, by Top Global University Project, Waseda University and the Project PRA 2018 49 of University of Pisa . MI is supported by JST CREST Grant Number JPMJCR1913 and by JSPS KAKENHI Grant Number JP19K14581 . Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2022",
month = jun,
day = "5",
doi = "10.1016/j.jde.2022.03.008",
language = "English",
volume = "321",
pages = "258--295",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
}