| Author | dc.contributor.author | Pino Manresa, Manuel del | |
| Author | dc.contributor.author | Kowalczyk, Michal | es_CL |
| Author | dc.contributor.author | Pacard, Frank | es_CL |
| Author | dc.contributor.author | Wei, Juncheng | es_CL |
| Admission date | dc.date.accessioned | 2010-06-17T14:36:13Z | |
| Available date | dc.date.available | 2010-06-17T14:36:13Z | |
| Publication date | dc.date.issued | 2010 | |
| Identifier | dc.identifier.uri | https://repositorio.uchile.cl/handle/2250/125345 | |
| Abstract | dc.description.abstract | We construct a new class of positive solutions for the classical elliptic problem
¢u ¡ u + up = 0; p > 2; in R2:
We establish a deep relation between them and the following Toda system
c2f00 j = efj¡1¡fj ¡ efj¡fj+1 in R; j = 1; : : : ; k:
We show that these solutions have the approximate form u(x; z) » Pk
j=1 w(x ¡ fj(z))
where w is the unique even, positive, asymptotically vanishing solution of w00 ¡ w +
wp = 0 in R. Functions fj(z), representing the multiple ends of u(x; z), solve the
aforementioned Toda system, they are even, asymptotically linear, with
f0 ´ ¡1 < f1 ¿ ¢ ¢ ¢ ¿ fk < fk+1 ´ +1:
The solutions of the elliptic problem we construct have their counterpart in the
theory of constant mean curvature surfaces. An analogy can also be made between
their construction and the gluing of constant scalar curvature Fowler singular metrics
in the sphere. | en_US |
| Patrocinador | dc.description.sponsorship | This work has been partly supported by chilean research
grants Fondecyt 1070389, 1050311, FONDAP, Nucleus Millennium grant P04-069-F,
an Ecos-Conicyt contract and an Earmarked Grant from RGC of Hong Kong. | en_US |
| Lenguage | dc.language.iso | en | en_US |
| Título | dc.title | The Toda system and multiple-end solutions of autonomous planar elliptic problems | en_US |
| Document type | dc.type | Artículo de revista | |
