New blow-up phenomena for SU(n+1) Toda system
Analysis of PDEs
2016-04-14 v2
Abstract
We consider the Toda system (S_\lambda) \quad \left\{ \begin{aligned} & \Delta u_1 + 2\lambda e^{u_1} - \lambda e^{u_2}- \dots - \lambda e^{u_k} = 0\quad \hbox{in}\ \Omega,\\ & \Delta u_2 - \lambda e^{u_1} + 2\lambda e^{u_2} - \dots - \lambda e^{u_k}=0\quad \hbox{in}\ \Omega,\\ &\vdots \hskip3truecm \ddots \hskip2truecm \vdots\\ & \Delta u_k -\lambda e^{u_1}-\lambda e^{u_2}- \dots+2\lambda e^{u_k}=0\quad \hbox{in}\ \Omega, &u_1 = u_2 = \dots = u_k =0 \quad \hbox{on}\ \partial\Omega.\\ \end{aligned}\right. If and is symmetric with respect to the origin, we construct a family of solutions to such that the th component blows-up at the origin with a mass as goes to zero.
Keywords
Cite
@article{arxiv.1402.3784,
title = {New blow-up phenomena for SU(n+1) Toda system},
author = {Monica Musso and Angela Pistoia and Juncheng Wei},
journal= {arXiv preprint arXiv:1402.3784},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1210.5719