5 papers
A flow approach to the Toda system
Yong Luo, Linlin Sun, Guofang Wang
In this paper we introduce a flow to study the Toda system, which we call {\it Toda flow.} More generally, we introduce a flow of the Liouville systems, formulated as a coupled par…
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} -Îu = Ï_1\left(\frac{h_1e^…
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…
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} -Îu_1 = 2Ï_1(h_1e^{u_1}-1) - Ï_2(h_2e^{u_2}-1),\\ -Îu_2 = 2Ï…
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} -Îu_1 = 2Ï_1(h_1e^{u_1}-1) - Ï_2(h_2e^{u_2}-1),\\ -Îu_2 = 2Ï_2(h_2e^{u_…