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PASQUALE CANDITO

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

  • Autori: Candito, Pasquale; Marano, Salvatore A.; Perera, Kanishka
  • Anno di pubblicazione: 2015
  • Tipologia: Articolo in rivista
  • OA Link: http://hdl.handle.net/10447/672926

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.