Concentration of Solutions for a Singularly Perturbed Neumann Problem in non smooth domains

Abstract

We consider the equation $-\epsilon^{2}\Delta u + u = u^ {p}$ in a bounded domain $\Omega\subset\R^{3}$ 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.