Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions

2024/03/30 by Yohei Fujishima, Fujishima, Yohei, Norisuke Ioku +5 · 4 citations
Computer Science · Mathematics · #35A24 #35B40 #35J61 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2404.00258

openalex publication_date 2024/03/30 · openalex created_date 2024/04/03 · openalex updated_date 2026/07/28

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.

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• Classification of bifurcation structure for semilinear elliptic equations in a ball
• Infinite concentration and oscillation estimates for supercritical semilinear elliptic equations in discs. II
• Infinite concentration and oscillation estimates for supercritical semilinear elliptic equations in discs. I

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