@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 {2008,
	title = {Entire solutions of autonomous equations on Rn with nontrivial asymptotics},
	journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72},
	year = {2008},
	abstract = {We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic.},
	url = {http://hdl.handle.net/1963/2640},
	author = {Andrea Malchiodi}
}
@article {2008,
	title = {Existence of conformal metrics with constant $Q$-curvature},
	journal = {Ann. of Math. 168 (2008) 813-858},
	number = {SISSA;70/2004/M},
	year = {2008},
	abstract = {Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.},
	url = {http://hdl.handle.net/1963/2308},
	author = {Zindine Djadli and Andrea Malchiodi}
}
@mastersthesis {2000,
	title = {Existence and multiplicity results for some problems in Riemannian geometry},
	year = {2000},
	school = {SISSA},
	keywords = {Yamabe problem},
	url = {http://hdl.handle.net/1963/5948},
	author = {Andrea Malchiodi}
}
