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.