@article {bonheure2012concentration, title = {Concentration on circles for nonlinear Schr{\"o}dinger{\textendash}Poisson systems with unbounded potentials vanishing at infinity}, journal = {Communications in Contemporary Mathematics}, volume = {14}, number = {02}, year = {2012}, pages = {1250009}, publisher = {World Scientific}, abstract = {

The present paper is devoted to weighted nonlinear Schr{\"o}dinger{\textendash}Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

}, doi = {10.1142/S0219199712500095}, url = {https://doi.org/10.1142/S0219199712500095}, author = {Bonheure, Denis and Di Cosmo, Jonathan and Mercuri, Carlo} } @article {bonheure2011embedding, title = {Embedding theorems and existence results for nonlinear Schr{\"o}dinger{\textendash}Poisson systems with unbounded and vanishing potentials}, journal = {Journal of Differential Equations}, volume = {251}, number = {4-5}, year = {2011}, pages = {1056{\textendash}1085}, publisher = {Elsevier}, abstract = {

Motivated by existence results for positive solutions of non-autonomous nonlinear Schr{\"o}dinger{\textendash}Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

}, doi = {10.1016/j.jde.2011.04.010}, url = {https://doi.org/10.1016/j.jde.2011.04.010}, author = {Bonheure, Denis and Mercuri, Carlo} } @article {mercuri2010global, title = {A global compactness result for the p-Laplacian involving critical nonlinearities}, journal = {Discrete \& Continuous Dynamical Systems-A}, volume = {28}, number = {2}, year = {2010}, pages = {469{\textendash}493}, abstract = {
We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

}, doi = {10.3934/dcds.2010.28.469}, url = {http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5097}, author = {Mercuri, Carlo and Willem, Michel} } @article {fall2009foliations, title = {Foliations of small tubes in Riemannian manifolds by capillary minimal discs}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {70}, number = {12}, year = {2009}, pages = {4422{\textendash}4440}, publisher = {Elsevier}, abstract = {

Letting\ Γ\ be an embedded curve in a Riemannian manifold\ M, we prove the existence of minimal disc-type surfaces centered at\ Γinside the surface of revolution of\ M\ around\ Γ, having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

}, doi = {10.1016/j.na.2008.10.024}, url = {https://doi.org/10.1016/j.na.2008.10.024}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} } @article {fall2009minimal, title = {Minimal disc-type surfaces embedded in a perturbed cylinder}, journal = {Differential and Integral Equations}, volume = {22}, number = {11/12}, year = {2009}, pages = {1115{\textendash}1124}, publisher = {Khayyam Publishing, Inc.}, abstract = {

In the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

}, url = {https://projecteuclid.org/euclid.die/1356019407}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} } @article {mercuri2008positive, title = {Positive solutions of nonlinear Schr{\"o}dinger-Poisson systems with radial potentials vanishing at infinity}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl}, volume = {19}, number = {3}, year = {2008}, pages = {211{\textendash}227}, publisher = {Citeseer}, abstract = {

We deal with a weighted nonlinear Schr{\textasciidieresis}odinger-Poisson system, allowing the potentials to vanish at infinity.

}, doi = {10.1.1.510.3635}, url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635\&rep=rep1\&type=pdf}, author = {Mercuri, Carlo} }