Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 64, pp. 1-13.

Title: Local well-posedness and standing waves with prescribed mass for
Schrodinger-Poisson systems with a logarithmic potential in R^2 
       
Authors: Xuechao Dou (Shandong Univ. of Technology, China)
         Juntao Sun  (Shandong Univ. of Technology, China)
         
Abstract: 
In this article, we consider  planar Schrodinger-Poisson systems
with  a logarithmic external potential $W(x)=\ln (1+|x|^2)$ and a general
nonlinear term $f$. We obtain conditions for the local well-posedness of
the Cauchy problem in the energy space. By introducing some suitable assumptions on $f$, 
we prove the existence of the global minimizer. In addition, with the
help of the local well-posedness, we show that the set of ground state
standing waves is orbitally stable.

Submitted May 6, 2023. Published September 25, 2023.
Math Subject Classifications: 35J20, 35J60.
Key Words: Nonlinear Schrodinger-Poisson system; normalized solution;
 logarithmic external potential; local well-posedness.