In this talk we consider the equation $-\Delta u +\lambda u- u^{\frac{n-k+2}{n-k-2}} =0\,\hbox{ in }\,\O \subset\,\R^{n}$, under zero Neumann boundary conditions, where $\O$ is open, smooth and bounded and where $\lambda$ is a positive and large real number. We prove existence of positive solutions concentrating along a submanifold $K$ of the boundary $\partial\O$ with dim $(K) = k$, as $\lambda\to\,+\infty$. This is a joint work with M. del Pino and F. Mahmoudi.