Concentration phenomena for the Schrodinger-Poisson system in R2

We perform a semiclassical analysis for the planar Schrodinger-Poisson system where $arepsilon$ is a positive parameter corresponding to the Planck constant and $V$ is a bounded external potential. We detect solution pairs~$(u_arepsilon, E_arepsilon)$ of the system $(SP_arepsilon)$ as~$ge ightarrow 0$, leaning on a nongeneracy result in a recent paper by Bonheure, Cingolani and Van Schaftingen