A critical phenomenon for sublinear elliptic equations in cone-like domains
Vladimir Kondratiev, Vitali Liskevich, Vitaly Moroz, Zeev Sobol
Abstract
We study positive supersolutions to an elliptic equation
(∗)
:
−Δu=c|x
|
−s
u
p
,
p,s∈R
in cone-like domains in
R
N
(
N≥2
). We prove that in the sublinear case
p<1
there exists a critical exponent
p
∗
<1
such that equation
(∗)
has a positive supersolution if and only if
−∞<p<
p
∗
. The value of
p
∗
is determined explicitly by
s
and the geometry of the cone.