  We provide the structure of regular/singular fast/slow decay radially
symmetric solutions for a class of superlinear elliptic equations with an in-
definite weight on the nonlinearity f (u, r). In particular we are interested
in the case where f is positive in a ball and negative outside, or in the re-
versed situation. We extend the approach to elliptic equations in presence of
Hardy potentials. By the use of Fowler transformation we study the
corresponding dynamical systems, presenting the construction of invariant
manifolds when the global existence of solutions is not ensured.
