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On a class of critical (p, q)-Laplacian problems

  • Pasquale Candito
  • Salvatore A. Marano
  • Kanishka Perera
Article

Abstract

We obtain nontrivial solutions of a critical (p, q)-Laplacian problem in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical Sobolev exponents, this problem lacks a direct sum decomposition suitable for applying the classical linking theorem. We show that every Palais–Smale sequence at a level below a certain energy threshold admits a subsequence that converges weakly to a nontrivial critical point of the variational functional. Then we prove an abstract critical point theorem based on a cohomological index and use it to construct a minimax level below this threshold.

Keywords

(p, q)-Laplacian problems Critical Sobolev exponent Nontrivial solutions Critical point theory Cohomological index 

Mathematics Subject Classification

Primary 35J92 35B33 Secondary 58E05 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Pasquale Candito
    • 1
  • Salvatore A. Marano
    • 2
  • Kanishka Perera
    • 3
  1. 1.Università degli Studi di Reggio CalabriaReggio CalabriaItaly
  2. 2.Università degli Studi di CataniaCataniaItaly
  3. 3.Florida Institute of TechnologyMelbourneUSA

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