Existence and uniqueness of constraint minimizers for the planar Schrodinger-Poisson system with logarithmic potentials

作者：Guo, Yujin^*; Liang, Wenning; Li, Yan

来源：Journal of Differential Equations, 2023, 369: 299-352.

DOI：10.1016/j.jde.2023.06.007

• Schrodinger-Poisson system
• Constraint minimizers
• Logarithmic convolution potential
• Logarithmic external potential
• Local uniqueness

In this paper, we study constraint minimizers u of the planar Schrodinger-Poisson system with a logarithmic convolution potential ln |x| * u2 and a logarithmic external potential V (x) = ln(1 + |x|2), which can be described by the L2-critical constraint minimization problem with a subcritical perturbation. We prove that there is a threshold p* e (0, co) such that constraint minimizers exist if and only if 0 < p < p*. In particular, the local uniqueness of positive constraint minimizers as p J' p* is analyzed by overcoming the sign-changing property of the logarithmic convolution potential and the non-invariance under translations of the logarithmic external potential. & COPY; 2023 Elsevier Inc.