### 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) |
---|---|

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 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Computational and Applied Mathematics*, vol. 131, no. 1-2, pp. 299-319. https://doi.org/10.1016/S0377-0427(00)00266-1

}

TY - JOUR

T1 - A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains

AU - Costa, David G.

AU - Ding, Zhonghai

AU - Neuberger, John M

PY - 2001/6/1

Y1 - 2001/6/1

N2 - 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.

AB - 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.

KW - Finite element method

KW - High-linking algorithm

KW - Modified mountain pass algorithm

KW - Sign-changing solution

KW - Superlinear elliptic equation

UR - http://www.scopus.com/inward/record.url?scp=0035361440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035361440&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(00)00266-1

DO - 10.1016/S0377-0427(00)00266-1

M3 - Article

AN - SCOPUS:0035361440

VL - 131

SP - 299

EP - 319

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1-2

ER -