Existence of normalized solutions for the planar Schrödinger-Poisson system with exponential critical nonlinearity

Abstract

In the present work we are concerned with the existence of normalized solutions to the following Schrödinger-Poisson System $$ \left\{ \begin{array}{ll} -Δu + λu + μ(\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ \ in \ } \mathbb{R}^2 , \\ \intR |u(x)|^2 dx = c,\ c> 0 , \end{array} \right. $$ for $\mu \in \mathbb{R}$ and a nonlinearity $f$ with exponential critical growth. Here $\lambda \in \mathbb{R}$ stands as a Lagrange multiplier and it is part of the unknown. Our main results extend and/or complement some results found in \cite{Ji} and \cite{[cjj]}.