Calculus of Variations and Geometric Measure Theory

S. Dovetta - L. Tentarelli

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

created by tentarelli on 07 Jul 2022


Published Paper

Inserted: 7 jul 2022
Last Updated: 7 jul 2022

Journal: Oper. Theory Adv. Appl.
Volume: 281
Pages: 113-125
Year: 2020
Doi: 10.1007/978-3-030-44097-8_5

ArXiv: 1803.09246 PDF

Volume "Discrete and Continuous Models in the Theory of Networks".


The paper aims at giving a first insight on the existencenonexistence 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.