On the two-dimensional Gierer-Meinhardt system with strong coupling

Authors
Wei, JC Winter, M
Citation
Jc. Wei et M. Winter, On the two-dimensional Gierer-Meinhardt system with strong coupling, SIAM J MATH, 30(6), 1999, pp. 1241-1263
Citations number
46
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN journal
00361410 → ACNP
Volume
30
Issue
6
Year of publication
1999
Pages
1241 - 1263
Database
ISI
SICI code
0036-1410(19991013)30:6<1241:OTTGSW>2.0.ZU;2-X
Abstract
We construct solutions with a single interior condensation point for the tw o-dimensional Gierer-Meinhardt system with strong coupling. The condensatio n point is located at a nondegenerate critical point of the diagonal part o f the regular part of Green's function for -Delta + 1 under the Neumann bou ndary condition. Our method is based on the Liapunov-Schmidt reduction for a system of elliptic equations.