Qualitative analysis for Moser-Trudinger nonlinearities with a low energy

Peng Luo, Kefan Pan, Shuangjie Peng

We are concerned with the Moser-Trudinger problem \begin{equation*} \begin{cases} -Δu=λue^{u^2}~~&\mbox{in}~Ω,\\[0.5mm] u>0 ~~ &{\text{in}~Ω},\\[0.5mm] u=0~~&\mbox{on}~\partial Ω,…