205 research outputs found
New blow-up phenomena for SU(n+1) Toda system
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.Comment: arXiv admin note: text overlap with arXiv:1210.571
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