Local well-posedness and standing waves with prescribed mass for Schrodinger-Poisson systems with a logarithmic potential in R^2

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. For more information see https://ejde.math.txstate.edu/Volumes/2023/64/abstr.html