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 |
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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 journal › Article
}
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 -