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Boundary concentration of a Gauged nonlinear Schrödinger equation on large balls

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Abstract

This paper is motivated by a gauged Schrödinger equation in dimension 2 including the so-called Chern–Simons term. The radially symmetric case leads to an elliptic problem with a nonlocal defocusing term, in competition with a local focusing nonlinearity. In this work we pose the equations in a ball under homogeneous Dirichlet boundary conditions. By using singular perturbation arguments we prove existence of solutions for large values of the radius. Those solutions are located close to the boundary and the limit profile is given.

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Acknowledgments

This work has been partially carried out during a stay of A. P. in Granada. He would like to express his deep gratitude to the Departamento de Análisis Matemático for the support and warm hospitality.

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Authors and Affiliations

  1. Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125 , Bari, Italy

    Alessio Pomponio

  2. Dpto. Análisis Matemático, 18071 , Granada, Spain

    David Ruiz

Authors
  1. Alessio Pomponio
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  2. David Ruiz
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Corresponding author

Correspondence to David Ruiz.

Additional information

Communicated by A. Malchiodi.

A. P. is supported by M.I.U.R.–P.R.I.N. “Metodi variazionali e topologici nello studio di fenomeni non lineari”, by GNAMPA Project “Metodi Variazionali e Problemi Ellittici Non Lineari” and by FRA2011 “Equazioni ellittiche di tipo Born-Infeld”. D. R. is supported by the Spanish Ministry of Science and Innovation under Grant MTM2011-26717 and by J. Andalucia (FQM 116).

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Pomponio, A., Ruiz, D. Boundary concentration of a Gauged nonlinear Schrödinger equation on large balls. Calc. Var. 53, 289–316 (2015). https://doi.org/10.1007/s00526-014-0749-2

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  • DOI: https://doi.org/10.1007/s00526-014-0749-2

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