Nodal solutions of a NLS equation concentrating on lower dimensional spheres

Abstract

In this work we deal with a following nonlinear Schrodinger equation in dimension greater or equal to 3, with a subcritical power-type nonlinearity and a positive potential satisfying a local condition. We prove the existence and concentration of nodal solutions which concentrate around a k - dimensional sphere of RN, where k is between 1 and N-1, as a parameter goes to 0. The radius of such sphere is related with the local minimum of a function which takes into account the potential. Variational methods are used together with the penalization technique in order to overcome the lack of compactness.