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arXiv · 2011.00276

Ground states for the NLS equation with combined nonlinearities on non-compact metric graphs

Dario Pierotti·Nicola Soave
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Abstract

We investigate the existence of ground states with prescribed mass for the NLS energy with combined $L^2$-critical and subcritical nonlinearities, on a general non-compact metric graph $\mathcal{G}$. The interplay between the different nonlinearities creates new phenomena with respect to purely critical or subcritical problems on graphs; from a different perspective, topological and metric properties of the underlying graph drastically influence existence and non-existence of ground states with respect to the analogue problem on the real line.

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Dario Pierotti, Nicola Soave. 2020-10-31. Ground states for the NLS equation with combined nonlinearities on non-compact metric graphs. https://arxiv.org/abs/2011.00276

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