@article {2011, title = {Critical points of the Moser-Trudinger functional}, number = {SISSA;46/2011/M}, year = {2011}, institution = {SISSA}, keywords = {Moser-Trudinger inequality}, url = {http://hdl.handle.net/1963/4592}, author = {Francesca De Marchis and Andrea Malchiodi and Luca Martinazzi} } @article {de2011multiplicity, title = {Multiplicity of solutions for a mean field equation on compact surfaces}, journal = {Boll. Unione Mat. Ital.(9)}, volume = {4}, year = {2011}, pages = {245{\textendash}257}, abstract = {

We consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

}, author = {Francesca De Marchis} } @article {2011, title = {Supercritical conformal metrics on surfaces with conical singularities}, journal = {Int Math Res Notices (2011) 2011 (24): 5625-5643}, number = {SISSA;56/2010/M}, year = {2011}, publisher = {Oxford University Press}, abstract = {

We study the problem of prescribing the Gaussian curvature on surfaces with conical singularities in supercritical regimes. Using a Morse-theoretical approach we prove a general existence theorem on surfaces with positive genus, with a generic multiplicity result.

}, doi = {10.1093/imrn/rnq285}, url = {http://hdl.handle.net/1963/4095}, author = {Mauro Bardelloni and Francesca De Marchis and Andrea Malchiodi} } @article {DEMARCHIS20102165, title = {Generic multiplicity for a scalar field equation on compact surfaces}, journal = {Journal of Functional Analysis}, volume = {259}, number = {8}, year = {2010}, pages = {2165 - 2192}, abstract = {

We prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

}, keywords = {Generic multiplicity, Geometric PDE{\textquoteright}s, Morse inequalities, Scalar field equations}, issn = {0022-1236}, doi = {https://doi.org/10.1016/j.jfa.2010.07.003}, url = {http://www.sciencedirect.com/science/article/pii/S0022123610002697}, author = {Francesca De Marchis} }