Nodal solutions of an NLS equation concentrating on lower dimensional spheres

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2015-12-26

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In this work we deal with the following nonlinear Schrödinger equation: {−<sup>ϵ2</sup>Δu+V(x)u=f(u)in <sup>RN</sup>u∈<sup>H1</sup>(<sup>RN</sup>),(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<sup>N</sup>, 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.

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concentration on manifolds, nodal solutions, variational methods

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Boundary Value Problems, v. 2015, n. 1, 2015.

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