arXiv Analytics

Sign in

arXiv:1803.09246 [math.AP]AbstractReferencesReviewsResources

Ground states of the $L^2$-critical NLS equation with localized nonlinearity on a tadpole graph

Simone Dovetta, Lorenzo Tentarelli

Published 2018-03-25, updated 2018-11-19Version 2

The paper aims at giving a first insight on the existence/nonexistence of ground states for the $L^2$-critical NLS equation on metric graphs with localized nonlinearity. In particular, we focus on the tadpole graph, which, albeit being a toy model, allows to point out some specific features of the problem, whose understanding will be useful for future investigations.

Comments: 12 pages, 5 figures. Keywords: minimization, metric graphs, critical growth, nonlinear Schr\"odinger equation, localized nonlinearity
Journal: Oper. Theory Adv. Appl. 281 (2020), 113-125
Categories: math.AP
Subjects: 35R02, 35Q55, 81Q35, 49J40
Related articles: Most relevant | Search more
arXiv:1811.02387 [math.AP] (Published 2018-11-06)
$L^2$-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features
arXiv:1612.07914 [math.AP] (Published 2016-12-23)
Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension
arXiv:2203.06702 [math.AP] (Published 2022-03-13)
Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect

Links

Toolbox