Refined spike profiles of constraint minimizers for the planar Schrödinger-Poisson system with logarithmic potentials.

This paper is concerned with constraint minimizers of the planar Schrödinger-Poisson system with a logarithmic convolution potential and a logarithmic external potential $ V(x) = \ln(1+|x|^2) $. It is known that minimizers exist if and only if the particle mass $ \rho>0 $ satisfies $ \rho<\rho^* $ for some threshold $ \rho^*\in(0,\infty) $. As a continuation of [22], this paper is devoted to analyzing the refined spike profiles of constraint minimizers as $ \rho\nearrow\rho^* $. [ABSTRACT FROM AUTHOR]