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Multiplicity of Semiclassical States Solutions for a Weakly Coupled Schrödinger System with Critical Growth in Divergent Form

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Abstract

In this paper we prove existence of multiple solutions for the critical gradient elliptic system

where the potentials a,f,b,g are continuous, the nonlinearity Q has subcritical growth and the nonlinearity K has critical growth. For suitable hypotheses on a,f,b,g and Q,K we are able to prove multiplicity of solutions for this system involving category theory and concentration of theses solutions around some especial points related with the potentials a and b.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Brasília, 70910-900, Brasília, DF, Brazil

    Giovany M. Figueiredo & Segundo Manuel A. Salirrosas

Authors
  1. Giovany M. Figueiredo
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  2. Segundo Manuel A. Salirrosas
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Correspondence to Giovany M. Figueiredo.

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Research was partially supported by CNPq/Brazil, FAP-DF and CAPES.

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Figueiredo, G.M., Salirrosas, S.M.A. Multiplicity of Semiclassical States Solutions for a Weakly Coupled Schrödinger System with Critical Growth in Divergent Form. Potential Anal 59, 237–261 (2023). https://doi.org/10.1007/s11118-021-09966-5

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  • DOI: https://doi.org/10.1007/s11118-021-09966-5

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