Nodal solutions of an NLS equation concentrating on lower dimensional spheres

• Autor(a) principal: Figueiredo, Giovany M
• Data de Publicação: 2015
• Outros Autores: Pimenta, Marcos T. O. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1186/s13661-015-0411-8; http://hdl.handle.net/11449/168040
• topic: concentration on manifolds; nodal solutions; variational methods

In this work we deal with the following nonlinear Schrödinger equation: {−^ϵ2Δu+V(x)u=f(u)in ^RNu∈^H1(^RN),(Formula presented.) 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 (Formula presented.). 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.