Blow-up rates of large solutions for semilinearelliptic equations
Zhijun Zhang, Ling Mi · Communications on Pure & Applied Analysis · 2011
In this paper we analyze the blow-up rates of large solutions tothe semilinear elliptic problem $\Delta u =b(x)f(u), x\in \Omega, u|_{\partial \Omega} = +\infty,$ where $\Omega$ is a bounded domain with smooth boundaryin $R^N$, $f$ is rapidly varying or normalised regularly varying with index $p$ ($p>1$) at infinity, and $b \inC^\alpha (\bar{\Omega})$ which is non-negative in $\Omega$ and positivenear the boundary and may be vanishing on the boundary.