SU(3) Chern-Simons vortex theory and Toda systems

摘要

Motivated by the study of the asymptotic properties of "non-topological" condensates in the non-abelian Chern-Simons vortex theory (see [26]), we analyze the SU(3) Toda system: [GRAPHICS] where M = R-2/Z(2), K = (k(ij)) = [GRAPHICS] is the SU(3) Cartan matrix and lambdaj are positive parameters. We study the variational problem associated with the system (P)lambda(1)lambda(2) in a range of parameters, where the trivial solution is a strict local minimum and the corresponding Sobolev-type inequality fails to apply. In this situation, a lack of compactness may occur due to concentration phenomena. Nonetheless, we are able to establish the existence of a non-trivial solution for (P)lambda(1)lambda(2) which is not a minimizer. (C) 2002 Elsevier Science (USA) [References: 37]