Monday, May 6, 2024 — 12:00 pm — laboratorio M0.2, edificio Matematica
Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions
Abstract: In this talk, we consider singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities by introducing a new classification of the growth rate of exponential functions. The strategy is to introduce a model nonlinearity which admits an explicit singular solution. Then, using a transformation, one obtains an approximate singular solution, and then one concludes by a suitable fixed point argument. Our method covers a wide class of nonlinearities in a unified way. As a special case, our result contains a pioneering contribution by Ibrahim–Kikuchi–Nakanishi–Wei for the Moser–Trudinger type nonlinearity. This talk is based on a joint work with Yohei Fujishima, Bernhard Ruf, and Elide Terraneo.