Nonradial singular solutions for elliptic equations with exponential nonlinearity-Reference-Cited by-同舟云学术

Nonradial singular solutions for elliptic equations with exponential nonlinearity

Published:2024 Issue:5 Volume:32 Page:3171-3201
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Cao Jingyue,Shao Yunkang,Wan Fangshu,Wang Jiaqi,Zhu Yifei

Abstract

<abstract>For any $ R > 0 $, infinitely many nonradial singular solutions can be constructed for the following equation: <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation} -\Delta u = e^u \;\;\; \mbox{in}\; B_R \backslash \{0\} , \;\;\;\;\;\;(0.1)\end{equation} $\end{document} </tex-math></disp-formula> where $ B_R = \{x \in \mathbb{R}^N \; (N \geq 3): \; |x| < R\} $. To construct nonradial singular solutions, we need to consider asymptotic expansion at the isolated singular point $ x = 0 $ of a prescribed solution of (0.1). Then, nonradial singular solutions of (0.1) can be constructed by using the asymptotic expansion and introducing suitable weighted Hölder spaces.</abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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