Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains

Luigi Appolloni, Riccardo Molle

We consider the problem $-\hat{I}”u+\hat{I}»u=u^{p-1}$, where $u\in H_0^1(\hat{I}\text{c◯})$ verifies $\Vert u{\Vert }_{L^2}=m>0$, and $\hat{I}»\in [0,+\infty )$. Here, ${\mathbb{R}}^N\setminus \hat{I}\text{c◯}$ is nonempty and compact. We…