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math.AP2025
Critical mean field equations for equilibrium turbulence with sign-changing prescribed functions
Linlin Sun, Xiaobao Zhu
Let be a compact Riemann surface with unit area. We investigate the mean field equation for equilibrium turbulence: \begin{align} \begin{cases} -Δu = ρ_1\left(\frac{h_1e^{u…
math.AP2024
Existence results for Toda systems with sign-changing prescribed functions: Part II
Linlin Sun, Xiaobao Zhu
Let be a compact Riemann surface with area . 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 be a compact Riemann surface with area , 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)…