Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, part II

We study the equation −ε2∆u + V (|x|)u = up, with ε > 0 and p > 1, in balls or annuli of Rn, under Neumann or Dirichlet boundary conditions. As ε tends to zero we prove existence of radial solutions, with the profile of an interior onedimensional spike, concentrated near some sphere. Of particular interest are the different, or opposite, effects created by the Neumann or Dirichlet boundary conditions on the existence as well as the locations of the concentration sets of solutions.