Normalized solutions for planar Schrödinger-Poisson system with a positive potential
Normalized solutions for planar Schrödinger-Poisson system with a positive potential
In this paper, we investigate normalized solutions for the following Schrödinger-Poisson system with an $ L^2 $-constraint:$ \begin{equation*} \label{SP1} \left\{ \begin{array}{ll} -\Delta u+\lambda u+|x|^2u+\frac{1}{2\pi}\left(\ln|\cdot|\ast|u|^2\right)u = f(u), & x\in \mathbb{R}^2, \\ \int_{ \mathbb{R}^2}u^2\mathrm{d}x = c, \ \end{array} \right. \end{equation*} $where $ f\in \mathcal{C}( \mathbb{R}, \mathbb{R}) $, $ c>0 $ is a …