@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}
}
@article {2013,
	title = {A variational Analysis of the Toda System on Compact Surfaces},
	journal = {Communications on Pure and Applied Mathematics, Volume 66, Issue 3, March 2013, Pages 332-371},
	number = {arXiv:1105.3701;},
	year = {2013},
	note = {pre-peer version, to appear in Comm. Pure Applied Math},
	publisher = {Wiley},
	abstract = {In this paper we consider the Toda system of equations on a compact surface.
We will give existence results by using variational methods in a non coercive
case. A key tool in our analysis is a new Moser-Trudinger type inequality under
suitable conditions on the center of mass and the scale of concentration of the
two components u_1, u_2.},
	doi = {10.1002/cpa.21433},
	url = {http://hdl.handle.net/1963/6558},
	author = {Andrea Malchiodi and David Ruiz}
}
@article {ruiz2011,
	title = {Cluster solutions for the Schr{\"o}dinger-Poisson-Slater problem around a local minimum of the potential},
	journal = {Rev. Mat. Iberoamericana},
	volume = {27},
	number = {1},
	year = {2011},
	month = {01},
	pages = {253{\textendash}271},
	publisher = {Real Sociedad Matem{\'a}tica Espa{\~n}ola},
	url = {https://projecteuclid.org:443/euclid.rmi/1296828834},
	author = {David Ruiz and Giusi Vaira}
}
@article {2011,
	title = {New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces},
	journal = {Geometric and Functional Analysis 21 (2011) 1196-1217},
	number = {SISSA;74/2010/M},
	year = {2011},
	publisher = {Springer},
	abstract = {We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.},
	doi = {10.1007/s00039-011-0134-7},
	url = {http://hdl.handle.net/1963/4099},
	author = {Andrea Malchiodi and David Ruiz}
}
@article {2008,
	title = {Multiple bound states for the Schroedinger-Poisson problem},
	journal = {Commun. Contemp. Math. 10 (2008) 391-404},
	year = {2008},
	doi = {10.1142/S021919970800282X},
	url = {http://hdl.handle.net/1963/2679},
	author = {Antonio Ambrosetti and David Ruiz}
}
@article {2008,
	title = {Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn},
	journal = {J. Funct. Anal. 254 (2008) 2816-2845},
	number = {SISSA;73/2007/M},
	year = {2008},
	abstract = {Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schr{\"o}dinger equations.},
	doi = {10.1016/j.jfa.2007.11.013},
	url = {http://hdl.handle.net/1963/2175},
	author = {Antonio Ambrosetti and Giovanna Cerami and David Ruiz}
}
@article {2007,
	title = {Multi-bump solitons to linearly coupled systems of nonlinear Schr{\"o}dinger equations},
	number = {SISSA;29/2006/M},
	year = {2007},
	doi = {10.1007/s00526-006-0079-0},
	url = {http://hdl.handle.net/1963/1835},
	author = {Antonio Ambrosetti and Eduardo Colorado and David Ruiz}
}
@article {2006,
	title = {Bound states of Nonlinear Schroedinger Equations with  Potentials Vanishing at Infinity},
	journal = {J. Anal. Math. 98 (2006) 317-348},
	number = {SISSA;18/2005/M},
	year = {2006},
	doi = {10.1007/BF02790279},
	url = {http://hdl.handle.net/1963/1756},
	author = {Antonio Ambrosetti and Andrea Malchiodi and David Ruiz}
}
@article {2006,
	title = {Radial solutions concentrating on spheres of nonlinear Schr{\"o}dinger equations with vanishing potentials},
	journal = {Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907},
	number = {SISSA;38/2005/M},
	year = {2006},
	abstract = {We prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction.},
	doi = {10.1017/S0308210500004789},
	url = {http://hdl.handle.net/1963/1755},
	author = {Antonio Ambrosetti and David Ruiz}
}
