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{\it ``Bubble-Tower'' phenomena in a semilinear elliptic equation with mixed
  Sobolev growth} 

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{\bf Juan Campos}\\
 Universite de Chile\\
 email:  {\tt jcampos@dim.uchile.cl}\\
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\noindent {\bf Abstract}:  We consider the following problem 
         
$$\Delta u + u^p+u^q = 0 \in \mathbb{R}^N u > 0 \in \mathbb{R}^N
\lim_{\abs{x}\ {\rm to}\ \infty} u(x)\ {\rm to}\ 0$$ 

\noindent with $N/(N-2)< p < p^*=(N+2)/(N-2) < q , N> 2$.  We prove that if
$p$ is fixed, and $q$ is close enough to the  critical exponent $p^*$, then
there exists a radial solution which behaves like a superposition of bubbles
of different blow-up orders centered at the origin. Similarly when $q$ is
fixed and $p$ 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.

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