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

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

doi:10.1016/S0377-0427(00)00266-1

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

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

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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 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	https://doi.org/10.1016/S0377-0427(00)00266-1
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

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10.1016/S0377-0427(00)00266-1

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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.",

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AU - Neuberger, John M.

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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.

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