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

19 Citations (Scopus)

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

Fingerprint

Sign-changing Solutions
Numerical Investigation
Elliptic Equations
Nodal Curve
Mountain Pass
Criticality
Numerical Algorithms
Linking
Symmetry
Numerical Examples

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains. / Costa, David G.; Ding, Zhonghai; Neuberger, John M.

In: Journal of Computational and Applied Mathematics, Vol. 131, No. 1-2, 01.06.2001, p. 299-319.

Research output: Contribution to journalArticle

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