Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 64, pp. 1-9.
Title: A boundary blow-up for sub-linear elliptic problems with a
nonlinear gradient term
Author: Zhijun Zhang (Univ. Yantai, Shandong, China)
Abstract:
By a perturbation method and constructing comparison functions,
we show the exact asymptotic behaviour of solutions to
the semilinear elliptic problem
$$
\Delta u -|\nabla u|^q=b(x)g(u),\quad u>0 \quad\text{in }\Omega,
\quad u\big|_{\partial \Omega}=+\infty,
$$
where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth
boundary, $q\in (1, 2]$,
$g \in C[0,\infty)\cap C^1(0, \infty)$, $g(0)=0$,
$g$ is increasing on $[0, \infty)$,
and $b$ is non-negative non-trivial in $\Omega$,
which may be singular or vanishing on the boundary.
Submitted February 5, 2006. Published May 20, 2006.
Math Subject Classifications: 35J60, 35B25, 35B50, 35R05.
Key Words: Semilinear elliptic equations; large solutions;
asymptotic behaviour.