### 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 language | English (US) |
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Pages (from-to) | 299-319 |

Number of pages | 21 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 131 |

Issue number | 1-2 |

DOIs | |

State | Published - 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