Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains

Abstract

We consider the equation $-{ϵ}^2\mathrm{\Delta }u+u=u^p$ in a bounded domain $\Omega \subset {\mathbb{R}}^3$ with edges. We impose Neumann boundary conditions, assuming $1<p<5$, and prove concentration of solutions at suitable points of $\partial \Omega$ on the edges.