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Bibliographic Details
Main Authors: Colin, Mathieu, Watanabe, Tatsuya
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2411.02103
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Table of Contents:
  • This paper is devoted to the study of the nonlinear Schrödinger-Poisson system with a doping profile. We are interested in the existence of ground state solutions by considering the minimization problem on a Nehari-Pohozaev set. The presence of a doping profile causes several difficulties, especially in the proof of the uniqueness of a maximum point of a fibering map. A key ingredient is to establish the energy inequality. We also establish the relation between ground state solutions and $L^2$-constraint minimizers. 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.