A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains

David G. Costa, Zhonghai Ding, John M. Neuberger

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

In this paper, we investigate numerically sign-changing solutions of superlinear elliptic equations on symmetric domains. Based upon the symmetric criticality principle of Palais, the existence of sign-changing solutions which reflect the symmetry of Ω is studied first. A simple numerical algorithm, the modified mountain pass algorithm, is then proposed to compute the sign-changing solutions. This algorithm is discussed and compared with the high-linking algorithm for sign-changing solutions developed by Ding et al. [Nonlinear Anal. 37 (1999) 151-172]. By implementing both algorithms on several numerical examples, the sign-changing solutions and their nodal curves are displayed and discussed.

Original languageEnglish (US)
Pages (from-to)299-319
Number of pages21
JournalJournal of Computational and Applied Mathematics
Volume131
Issue number1-2
DOIs
StatePublished - Jun 1 2001

Keywords

  • Finite element method
  • High-linking algorithm
  • Modified mountain pass algorithm
  • Sign-changing solution
  • Superlinear elliptic equation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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