%0 Journal Article %J Communications in Contemporary Mathematics %D 2012 %T Concentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity %A Bonheure, Denis %A Di Cosmo, Jonathan %A Mercuri, Carlo %X

The present paper is devoted to weighted nonlinear Schrödinger–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.

%B Communications in Contemporary Mathematics %I World Scientific %V 14 %P 1250009 %G eng %U https://doi.org/10.1142/S0219199712500095 %R 10.1142/S0219199712500095 %0 Journal Article %J Journal of Differential Equations %D 2011 %T Embedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials %A Bonheure, Denis %A Mercuri, Carlo %X

Motivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–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.

%B Journal of Differential Equations %I Elsevier %V 251 %P 1056–1085 %G eng %U https://doi.org/10.1016/j.jde.2011.04.010 %R 10.1016/j.jde.2011.04.010