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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Nodal solutions of an NLS equation concentrating on lower dimensional spheres

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Figueiredo, Giovany M. [1] ; Pimenta, Marcos T. O. [2]
Total Authors: 2
[1] Fed Univ Para, Fac Matemat, BR-66075110 Belem, Para - Brazil
[2] Univ Estadual Paulista Unesp, Fac Ciencias & Tecnol, Dept Matemat & Computacao, BR-19060900 Presidente Prudente, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Web of Science Citations: 0

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)

FAPESP's process: 14/16136-1 - Study of semiclassical solutions to the stationary nonlinear Dirac equation
Grantee:Marcos Tadeu de Oliveira Pimenta
Support Opportunities: Regular Research Grants