Lorenzo Villata

The nonlinear Schr\"odinger equation on products of $\mathbb{R}^N$ and compact metric graphs

We study the stationary focusing nonlinear Schr\"odinger equation on the product $\mathbb{R}^N \times \mathcal{G}$ of the Euclidean space with a compact metric graph, in the mass-constrained variational setting. Such a product is a hybrid structure of a new type: all its faces are $(N+1)$-dimensional and are glued alon...