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Structure of the set of positive solutions of a non-linear Schrödinger equation

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Abstract

In this paper we study the existence, uniqueness and multiplicity of positive solutions to a non-linear Schr¨odinger equation. We describe the set of positive solutions. We use mainly the sub-supersolution method, bifurcation and variational arguments to obtain the results.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Brasília - UnB, CEP 70.910-900, Brasília - DF, Brazil

    Giovany M. Figueiredo

  2. Faculdade de Matemática, Universidade Federal do Pará, CEP: 66075-110, Belém - Pa, Brazil

    João R. Santos Júnior

  3. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C/. Tarfia s/n, 41012, Sevilla, Spain

    Antonio Suárez

Authors
  1. Giovany M. Figueiredo
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  2. João R. Santos Júnior
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  3. Antonio Suárez
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Correspondence to Antonio Suárez.

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Figueiredo, G.M., Santos Júnior, J.R. & Suárez, A. Structure of the set of positive solutions of a non-linear Schrödinger equation. Isr. J. Math. 227, 485–505 (2018). https://doi.org/10.1007/s11856-018-1752-7

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  • DOI: https://doi.org/10.1007/s11856-018-1752-7

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