Critical fractional p-Laplacian problems with possibly vanishing potentials

Marco Squassina, Kanishka Perera, Yang Yang

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We obtain nontrivial solutions of a critical fractional p-Laplacian equation in the whole space and with possibly vanishing potentials. In addition to the usual difficulty of the lack of compactness associated with problems involving critical Sobolev exponents, the problem is further complicated by the absence of a direct sum decomposition suitable for applying classical linking arguments. We overcome this difficulty using a generalized linking construction based on the Z2-cohomological index
Original languageEnglish
Pages (from-to)818-831
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume433
Publication statusPublished - 2016

Keywords

  • Vanishing potentials
  • fractional p-Laplacians

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