@article {BATTAGLIA2015937,
	title = {A general existence result for the Toda system on compact surfaces},
	journal = {Advances in Mathematics},
	volume = {285},
	year = {2015},
	pages = {937 - 979},
	abstract = {<p>In this paper we consider the following Toda system of equations on a compact surface:-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-Δu1=-4π∑j=1mα1,j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-Δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern{\textendash}Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation-Δu=ρ1(heu∫ΣheudVg-1)-ρ2(he-u∫Σhe-udVg-1), which arises in fluid dynamics."</p>},
	keywords = {Geometric PDEs, Min{\textendash}max schemes, Variational methods},
	issn = {0001-8708},
	doi = {https://doi.org/10.1016/j.aim.2015.07.036},
	url = {http://www.sciencedirect.com/science/article/pii/S0001870815003072},
	author = {Luca Battaglia and Aleks Jevnikar and Andrea Malchiodi and David Ruiz}
}
