On a general SU(3) Toda System

Abstract

We study the following generalized $SU(3)$ Toda System $$ \left\{\begin{array}{ll} -\Delta u=2e^u+\mu e^v & \hbox{ in }\R^2\\ -\Delta v=2e^v+\mu e^u & \hbox{ in }\R^2\\ \int_{\R^2}e^u<+\infty,\ \int_{\R^2}e^v<+\infty \end{array}\right. $$ where $\mu>-2$. We prove the existence of radial solutions bifurcating from the radial solution $(\log \frac{64}{(2+\mu) (8+|x|^2)^2}, \log \frac{64}{ (2+\mu) (8+|x|^2)^2})$ at the values $\mu=\mu_n=2\frac{2-n-n^2}{2+n+n^2},\ n\in\N $.