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>−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 Pohožaev-type identities."

VL - 270 UR - http://www.sciencedirect.com/science/article/pii/S0022123615004942 ER - TY - JOUR T1 - Entire solutions of autonomous equations on Rn with nontrivial asymptotics JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 Y1 - 2008 A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2640 U1 - 1483 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of conformal metrics with constant $Q$-curvature JF - Ann. of Math. 168 (2008) 813-858 Y1 - 2008 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2308 U1 - 1708 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Existence and multiplicity results for some problems in Riemannian geometry Y1 - 2000 A1 - Andrea Malchiodi KW - Yamabe problem PB - SISSA UR - http://hdl.handle.net/1963/5948 U1 - 5808 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER -