| Abstract: |
| In this talk, we consider the nonlinear Schr\odinger-Poisson system with a doping profile, which appears in the study of semi-conductor theory. We are interested in the existence of ground state solutions and their orbital stability.
The presence of a doping profile causes several difficulties, such as the proof of the strict sub-additivity and the uniqueness of a maximum point of a fibering map.When the doping profile is a characteristic function supported on
a bounded smooth domain, some geometric quantities related to the domain, such as the mean curvature, are responsible for the existence of ground state solutions. |
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