@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} }