Linlin Sun

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20232026

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math.AP2024

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

Linlin Sun, Xiaobao Zhu

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

math.AP2024

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)…

math.DG2024

Sinh-Gordon equations on finite graphs

Linlin Sun

In this paper, we focus on the sinh-Gordon equation on graphs. We introduce a uniform a priori estimate to define the topological degree for this equation with nonzero prescribed f…