Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 110, pp. 1-4.
Title: A remark on the existence of large solutions via
sub and supersolutions
Author: Jorge Garcia-Melian (Univ. de La Laguna, Spain)
Abstract:
We study the boundary blow-up elliptic problem
$\Delta u=a(x) f(u)$ in a smooth bounded domain
$\Omega\subset \mathbb{R}^N$, with $u|_{\partial\Omega}=+\infty$.
Under suitable growth assumptions on $a$ near $\partial\Omega$
and on $f$ both at zero and at infinity, we prove the existence
of at least a positive solution. Our proof is based on the
method of sub and supersolutions, which permits on the one hand
oscillatory behaviour of $f(u)$ at infinity and on the other hand
positive weights $a(x)$ which are unbounded and/or oscillatory
near the boundary.
Submitted July 4, 2003. Published November 4, 2003.
Math Subject Classifications: 35J60, 35J25.
Key Words: Boundary blow-up; sub and supersolutions