Multiplicity of symmetrically distinct sequences of solutions for a quasilinear problem in ℝn

Alexandru Kristály, Waclaw Marzantowicz

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The present paper is concerned with an elliptic problem in ℝN which involves the p-Laplacian, p > N, (N = 4 or N ≥ 6), while the nonlinear term has an oscillatory behaviour and is odd near an arbitrarily small neighborhood of the origin. A direct variational argument and a careful group-theoretical construction show the existence of at least [N-3/2] + (-1)N sequences of arbitrary small, non-radial, sign-changing solutions such that elements in different sequences are distinguished by their symmetry properties.

Original languageEnglish
Pages (from-to)209-226
Number of pages18
JournalNonlinear Differential Equations and Applications
Volume15
Issue number1-2
DOIs
Publication statusPublished - Apr 1 2008

Keywords

  • Oscillatory nonlinearity
  • P-Laplacian
  • Symmetrically distinct soltuions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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