Existence of five nonzero solutions with exact sign for A p-laplacian equation

Michael Filippakis, Alexandru Kristály, Nlkolaos S. Papageorgiou

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58 Citations (Scopus)


We consider nonlinear elliptic problems driven by the p-Laplacian with a nonsmooth potential depending on a parameter ? > 0. The main result guarantees the existence of two positive, two negative and a nodal (sign-changing) solution for the studied problem whenever ? belongs to a small interval (0,?*) and p ≥ 2. We do not impose any symmetry hypothesis on the nonlinear potential. The constant-sign solutions are obtained by using variational techniques based on nonsmooth critical point theory (minimization argument, Mountain Pass theorem, and a Brézis-Nirenberg type result for C1-minimizers), while the nodal solution is constructed by an upper-lower solutions argument combined with the Zorn lemma and a nonsmooth second deformation theorem.

Original languageEnglish
Pages (from-to)405-440
Number of pages36
JournalDiscrete and Continuous Dynamical Systems
Issue number2
Publication statusPublished - Jun 1 2009



  • Multiple solutions
  • Nodal solution
  • Non-smooth critical point theory
  • Positive solution
  • Upper-lower solutions
  • p-laplacian

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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