We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation:
-
εΔ
pu =
f(
x, u) in Ω,
where 1 <
p < ∞,
ε > 0 is a small parameter,
where
ω > 0,
a(
x) is a continuous function satisfying 0 <
a(
x) < 1 for
x ∈ Ω, Ω is a bounded smooth domain in R
N. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.