Abstract: We consider the following problem
with
. We prove that if
is fixed, and
is close enough to the critical exponent
, then
there exists a radial solution which behaves like a superposition of bubbles
of different blow-up orders centered at the origin. Similarly when
is
fixed and
is sufficiently close to the critic, we prove the existence of a
radial solution which resembles a superposition of flat bubbles centered at
the origin.