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

Michael Filippakis, A. Kristály, Nlkolaos S. Papageorgiou

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

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
Volume24
Issue number2
DOIs
Publication statusPublished - Jun 2009

Fingerprint

P-Laplacian Equation
Zorn's lemma
Constant-sign Solutions
Upper-lower Solutions
Nonsmooth Critical Point Theory
Nodal Solutions
Sign-changing Solutions
Mountain Pass Theorem
Nonlinear Elliptic Problems
P-Laplacian
Minimizer
Variational techniques
Symmetry
Interval
Theorem

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Existence of five nonzero solutions with exact sign for A p-laplacian equation. / Filippakis, Michael; Kristály, A.; Papageorgiou, Nlkolaos S.

In: Discrete and Continuous Dynamical Systems, Vol. 24, No. 2, 06.2009, p. 405-440.

Research output: Contribution to journalArticle

Filippakis, Michael ; Kristály, A. ; Papageorgiou, Nlkolaos S. / Existence of five nonzero solutions with exact sign for A p-laplacian equation. In: Discrete and Continuous Dynamical Systems. 2009 ; Vol. 24, No. 2. pp. 405-440.
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