where Ø is a smooth bounded domain of R with external normal ν, N ≥ 3, 1 < p < (N + 2)/(N − 2), J : R → R and V : R → R are C functions. In [5], the first author, extending the classical results by Ni and Takagi, in [3, 4], proved that there exist solutions of (1) that concentrate at maximum and minimum points of a suitable auxiliary function defined on the boundary ∂Ø and depending only on J a...

We consider a one-dimensional singularly perturbed transmission problem with two different diffusion coefficients. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high. We derive and analyze various finite element approaches for the approximation of the solution and conduct numerical computations that show the robustness (or lack there...