Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains

Luigi Appolloni, Riccardo Molle

We consider the problem $-\Delta u+\lambda u=u^{p-1}$, where $u\in H_0^1(\Omega )$ verifies $\Vert u{\Vert }_{L^2}=m>0$, and $\lambda \in [0,+\infty )$. Here, ${\mathbb{R}}^N\setminus \Omega$ is nonempty and compact. We prove…