Calculus of Variations and Geometric Measure Theory

L. Tentarelli

NLS ground states on metric graphs with localized nonlinearities

created by tentarelli on 07 Jul 2022


Published Paper

Inserted: 7 jul 2022
Last Updated: 7 jul 2022

Journal: J. Math. Anal. Appl.
Volume: 433
Number: 1
Pages: 291-304
Year: 2016
Doi: 10.1016/j.jmaa.2015.07.065

ArXiv: 1503.00455 PDF


We investigate the existence of ground states for the focusing subcritical NLS energy on metric graphs with localized nonlinearities. In particular, we find two thresholds on the measure of the region where the nonlinearity is localized that imply, respectively, existence or nonexistence of ground states. In order to obtain these results we adapt to the context of metric graphs some classical techniques from the Calculus of Variations.