@article {doi:10.1142/S0218202509003589, title = {Solutions of the Schr{\"o}dinger{\textendash}Poisson problem concentrating on spheres, part I: necessary conditions}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {19}, number = {05}, year = {2009}, pages = {707-720}, abstract = {

In this paper we study a coupled nonlinear Schr{\"o}dinger{\textendash}Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schr{\"o}dinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

}, doi = {10.1142/S0218202509003589}, url = {https://doi.org/10.1142/S0218202509003589}, author = {Ianni, Isabella and Giusi Vaira} }