On a general SU(3) Toda System

Abstract

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