Radially symmetric solutions in the self-dual Chern-Simons SU(3) model

초록

We briefly review the existence of radially symmetric non-topological solutions of an elliptic system arising from the self-dual SU(3) Chern-Simons model in ${\mathbb{R}}^2$. Non-topological solutions grow like logarithmic functions near $\infty$. We present some conditions on the growth rate under which radially symmetric non-topological solutions are bounded. Then we use the Leray-Schauder degree to prove the existence. By using the standard shooting argument, we will also show that there exist sequences of bubbling solutions unless we assume these conditions. This is a joint work with Prof. Namkwon Kim and Prof. Chang-Shou Lin.