Electron. J. Differential Equations, Vol. 2023 (2023), No. 64, pp. 1-13.

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

Xuechao Dou, Juntao Sun

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.
DOI: 10.58997/ejde.2023.64

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Xuechao Dou
School of Mathematics and Statistics
Shandong University of Technology
Shandong, Zibo 255049, China
email: xcdou178@163.com
Juntao Sun
School of Mathematics and Statistics
Shandong University of Technology
Shandong, Zibo 255049, China
email: jtsun@sdut.edu.cn

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