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Potential Analysis

, Volume 42, Issue 1, pp 229–246 | Cite as

Critical Points for a Functional Involving Critical Growth of Trudinger–Moser Type

  • João Marcos do Ó
  • Manassés de Souza
  • Everaldo de Medeiros
  • Uberlandio Severo
Article

Abstract

We establish the existence of critical points of leat energy for functionals associated with a class of singular quasilinear elliptic equations involving critical growth of Trudinger-Moser type. For this, in line with the Concentration–Compactness Principle due to P. -L. Lions (I. Rev. Mat. Iberoamericana 1, 145–201, 1985), we study the lack of compactness of Sobolev imbedding in Orlicz space defined in ℝ n (n ≥ 2).

Keywords

Critical points Least energy Concentration-compactness principle Trudinger–Moser inequality 

Mathematics Subject Classifications (2010)

35J60 35J20 35B33 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • João Marcos do Ó
    • 1
  • Manassés de Souza
    • 1
  • Everaldo de Medeiros
    • 1
  • Uberlandio Severo
    • 1
  1. 1.Departamento de MatemáticaUniversidade Federal da ParaíbaJoão PessoaBrazil

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