A note on boundary blow-up problem of $\Delta u=u^p$
Bull. Korean Math. Soc. 2019 Vol. 56, No. 1, 245-251
https://doi.org/10.4134/BKMS.b180221
Published online 2019 Jan 01
Seick Kim
Yonsei University
Abstract : 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
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