Existence results for Toda systems with sign-changing prescribed functions: Part I

LinLin Sun, Xiaobao Zhu

Let $(M,g)$ be a compact Riemann surface with area $1$, we shall study the Toda system $$ \begin{cases} -Δu_1 = 2ρ_1(h_1e^{u_1}-1) - ρ_2(h_2e^{u_2}-1),\\ -Δu_2 = 2ρ_2(h_2e^{u_2}-1)…