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