Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 02, pp. 1-8.

Title: Existence of large solutions for a semilinear elliptic
       problem via explosive sub- supersolutions
       
Author: Zhijun Zhang (Yantai Univ., Shandong, China)

Abstract: 
 We consider the boundary blow-up nonlinear elliptic problems
 $\Delta u\pm\lambda |\nabla u|^q=k(x)g(u)$  in a bounded
 domain with boundary condition $u|_{\partial \Omega}=+\infty$,
 where $q\in [0, 2]$ and $\lambda\geq0$.
 Under suitable growth assumptions on $k$ near the boundary
 and on  $g$ both at zero and at infinity, we show the existence
 of at least  one solution in $C^2(\Omega)$.
 Our proof is based on the method of  explosive sub-supersolutions,
 which permits positive weights $k(x)$ which are unbounded
 and/or oscillatory near the boundary. Also, we show
 the global optimal  asymptotic behaviour of the solution
 in some special cases.
 
Submitted May 21, 2005. Published January 6, 2006.
Math Subject Classifications: 35J60, 35B25, 35B50, 35R05.
Key Words: Semilinear elliptic equations;  explosive subsolutions; 
           explosive superbsolutions; existence;  
	   global optimal asymptotic behaviour.