On a general SU(3) Toda System

Abstract

We study the following generalized $SU(3)$ Toda System $$\{\begin{array}{ll}-\Delta u=2e^u+\mu e^v& in{\mathbb{R}}^2\\ -\Delta v=2e^v+\mu e^u& in{\mathbb{R}}^2\\ {\int }_{{\mathbb{R}}^2}{e}^u<+\infty ,{\int }_{{\mathbb{R}}^2}{e}^v<+\infty & \end{array}$$ 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 $\mu ={\mu }_n=2\frac{2-n-n^2}{2+n+n^2},n\in \mathbb{N}$.

References in corpus (1)

• Nonradial solutions for the Hénon equation in $R^N$