Radial solutions of the  equation  $u_t=\Delta u  +\lambda e^u$ on  an
$N$--dimensional ball, under Dirichlet  boundary condition are studied
for $3\le N\le 9$.  It is  shown that  global classical  solutions are
uniformly  bounded. Then     unbounded  global  $L^1$--solutions
are constructed as (nonclassical) connecting orbits between equilibria.