Nodal solutions of an NLS equation concentrating on lower dimensional spheres

In this work we deal with the following nonlinear Schrdinger equation: [-epsilon(2)Delta u + V(x) u = f (u) in R-N u is an element of H-1(R-N), where N >= 3, f is a subcritical power-type nonlinearity and V is a positive potential satisfying a local condition. We prove the existence and concentration of nodal solutions which concentrate around a k-dimensional sphere of R-N, where 1 <= k <= N-1, as epsilon -> 0. The radius of such a sphere is related with the local minimum of a function which takes into account the potential V. Variational methods are used together with the penalization technique in order to overcome the lack of compactness. (AU)