@article {BATTAGLIA20163750,
	title = {Existence and non-existence results for the SU(3) singular Toda system on compact surfaces},
	journal = {Journal of Functional Analysis},
	volume = {270},
	number = {10},
	year = {2016},
	pages = {3750 - 3807},
	abstract = {<p>We consider the SU(3) singular Toda system on a compact surface (Σ,g)-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑m=1Mα1m(δpm-1)-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑m=1Mα2m(δpm-1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim\&gt;-1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Poho{\v z}aev-type identities."</p>},
	keywords = {Liouville-type equations, Min{\textendash}max solutions, Non-existence results, Toda system},
	issn = {0022-1236},
	doi = {https://doi.org/10.1016/j.jfa.2015.12.011},
	url = {http://www.sciencedirect.com/science/article/pii/S0022123615004942},
	author = {Luca Battaglia and Andrea Malchiodi}
}
@article {BATTAGLIA201549,
	title = {Existence and multiplicity result for the singular Toda system},
	journal = {Journal of Mathematical Analysis and Applications},
	volume = {424},
	number = {1},
	year = {2015},
	pages = {49 - 85},
	abstract = {<p>We consider the Toda system on a compact surface (Σ,g)-Δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑j=1Jα1j(δpj-1),-Δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑j=1Jα2j(δpj-1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than -1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij{\textquoteright}s are allowed to be negative."</p>},
	keywords = {Existence result, Liouville-type equations, Multiplicity result, PDEs on compact surfaces, Toda system},
	issn = {0022-247X},
	doi = {https://doi.org/10.1016/j.jmaa.2014.10.081},
	url = {http://www.sciencedirect.com/science/article/pii/S0022247X14010191},
	author = {Luca Battaglia}
}
