Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions
Analysis of PDEs
2024-04-02 v1
Abstract
By introducing a new classification of the growth rate of exponential functions, singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities are constructed. The strategy is to introduce a model nonlinearity which admits an explicit singular solution. Then, using a transformation as in [8], 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 [15] for the Moser--Trudinger type nonlinearity.
Keywords
Cite
@article{arxiv.2404.00258,
title = {Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions},
author = {Yohei Fujishima and Norisuke Ioku and Bernhard Ruf and Elide Terraneo},
journal= {arXiv preprint arXiv:2404.00258},
year = {2024}
}