Electronic Journal of Differential Equations, 
Vol. 1995(1995), No. 10, pp 1--22. 

Title: Existence of Positive  Solutions for some Dirichlet Problems 
       with an Asymptotically Homogeneous Operator

Authors: Marta Garcia-Huidobro (Univ. Catolica de Chile)
         Raul Manasevich (Univ. de Chile)
         Pedro Ubilla (Univ. de Santiago de Chile)

Abstract: Existence of positive radially symmetric solutions to a 
Dirichlet problem of the form
 $${\rm div\,} (A(|Du|)Du)=f(u) { \rm in } \Omega $$ 
 $$       u = 0 		{ \rm on } \partial\Omega  $$
is studied by using blow-up techniques. It is proven here that by 
choosing the functions $sA(s)$ and $f(s)$ among a certain class called 
{\em asymptotically homogeneous}, 
the blow-up method still provides the a-priori bounds for positive
solutions. Existence is proved then by using degree theory.

Submitted February 12, 1995. Published August 11, 1995.
Math Subject Classification: 35J65.
Key Words: Dirichlet Problem; Positive Solution; Blow up.