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Existence of a ground state solution for a nonlinear scalar field equation with critical growth

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Abstract

In the present paper, we establish the existence of Ground State Solutions for some class of Elliptic problems with Critical Growth in \({\mathbb{R}^{N}}\) for N ≥ 2. Our results complete the study made in Berestycki and Lions (Arch Rat Mech Anal 82:313–346, 1983) and Berestycki, Gallouët and Kavian (C R Acad Sci Paris Ser I Math 297:307–310, 1984), in the sense that, in those papers only the subcritical growth was considered.

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Authors and Affiliations

  1. Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Rua Aprígio Veloso 882, CEP 58429-000, Campina Grande, PB, Brazil

    Claudianor O. Alves & Marco A. S. Souto

  2. Departamento de Matemática, Universidade Estadual de Campinas, IMECC, Rua Sérgio Buarque de Holanda, 651, CEP 13083-859, Campinas, SP, Brazil

    Marcelo Montenegro

Authors
  1. Claudianor O. Alves
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  2. Marco A. S. Souto
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  3. Marcelo Montenegro
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Correspondence to Marcelo Montenegro.

Additional information

Communicated by A. Malchiodi.

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Alves, C.O., Souto, M.A.S. & Montenegro, M. Existence of a ground state solution for a nonlinear scalar field equation with critical growth. Calc. Var. 43, 537–554 (2012). https://doi.org/10.1007/s00526-011-0422-y

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  • DOI: https://doi.org/10.1007/s00526-011-0422-y

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