Bull. Korean Math. Soc. 2019; 56(1): 245-251
Online first article June 28, 2018 Printed January 1, 2019
https://doi.org/10.4134/BKMS.b180221
Copyright © The Korean Mathematical Society.
Seick Kim
Yonsei University
Assume that $\Omega$ is a bounded domain in $\mathbb{R}^n$ with $n\ge 2$. We study positive solutions to the problem, $\Delta u=u^p$ in $\Omega$, $u(x)\to\infty$ as $x\to\partial\Omega$, where $p>1$. Such solutions are called boundary blow-up solutions of $\Delta u=u^p$. We show that a boundary blow-up solution exists in any bounded domain if $1
Keywords: blow-up, semi-linear equation, existence, uniqueness
MSC numbers: Primary 35J65; Secondary 35B05
Supported by: The author was partially supported by NRF Grant No. NRF-20151009350.
This paper is based on a presentation by the author at the 2001 AMS sectional meeting, Williamstown, MA, and was supported in
part by NSF Grant No. DMS-9971052.
2018; 55(1): 297-310
2016; 53(2): 335-350
2022; 59(1): 155-166
2021; 58(5): 1175-1192
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