@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 = {
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."
}, 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} }