| Abstract: |
| In this talk, we consider the nonlinear Schr\odinger-Poisson system. The aim of this talk is to present a complete characterization of the energy ground state solution for a critical strength of the interaction. Firstly, we prove the existence of an optimizer of the Gagliardo-Nirenberg-Coulomb inequality. Secondly, we give a full correspondence between an optimizer, an energy ground state solution and an action ground state solution. Finally, we obtain an explicit formula of the critical strength by using the optimizer and the best constant of the Gagliardo-Nirenberg-Coulomb inequality. |
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